LMFDB - Embedded newform 76.3.g.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(7,76)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("76.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.g (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 10x^{2} + 100 $ x^4 - 10*x^2 + 100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.1
Root			$-2.73861 + 1.58114i$ of defining polynomial
Character	$\chi$	$=$	76.7
Dual form			76.3.g.b.11.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-4.23861 + 2.44716i) q^{3} +4.00000 q^{4} +(1.73861 + 3.01137i) q^{5} +(-8.47723 + 4.89433i) q^{6} +10.0905i q^{7} +8.00000 q^{8} +(7.47723 - 12.9509i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-4.23861 + 2.44716i) q^{3} +4.00000 q^{4} +(1.73861 + 3.01137i) q^{5} +(-8.47723 + 4.89433i) q^{6} +10.0905i q^{7} +8.00000 q^{8} +(7.47723 - 12.9509i) q^{9} +(3.47723 + 6.02273i) q^{10} -17.5434i q^{11} +(-16.9545 + 9.78866i) q^{12} +(-3.00000 + 5.19615i) q^{13} +20.1810i q^{14} +(-14.7386 - 8.50934i) q^{15} +16.0000 q^{16} +(-2.52277 - 4.36957i) q^{17} +(14.9545 - 25.9019i) q^{18} +(2.28416 - 18.8622i) q^{19} +(6.95445 + 12.0455i) q^{20} +(-24.6931 - 42.7696i) q^{21} -35.0869i q^{22} +(27.6475 + 15.9623i) q^{23} +(-33.9089 + 19.5773i) q^{24} +(6.45445 - 11.1794i) q^{25} +(-6.00000 + 10.3923i) q^{26} +29.1430i q^{27} +40.3619i q^{28} +(-3.73861 + 6.47547i) q^{29} +(-29.4772 - 17.0187i) q^{30} +4.81544i q^{31} +32.0000 q^{32} +(42.9317 + 74.3598i) q^{33} +(-5.04555 - 8.73915i) q^{34} +(-30.3861 + 17.5434i) q^{35} +(29.9089 - 51.8037i) q^{36} -51.3861 q^{37} +(4.56832 - 37.7244i) q^{38} -29.3660i q^{39} +(13.9089 + 24.0909i) q^{40} +(17.4545 + 30.2320i) q^{41} +(-49.3861 - 85.5393i) q^{42} +(9.38613 - 5.41908i) q^{43} -70.1738i q^{44} +52.0000 q^{45} +(55.2950 + 31.9246i) q^{46} +(-19.1703 - 11.0680i) q^{47} +(-67.8178 + 39.1546i) q^{48} -52.8178 q^{49} +(12.9089 - 22.3589i) q^{50} +(21.3861 + 12.3473i) q^{51} +(-12.0000 + 20.7846i) q^{52} +(20.0455 - 34.7199i) q^{53} +58.2861i q^{54} +(52.8297 - 30.5012i) q^{55} +80.7238i q^{56} +(36.4772 + 85.5393i) q^{57} +(-7.47723 + 12.9509i) q^{58} +(-16.7614 + 9.67719i) q^{59} +(-58.9545 - 34.0374i) q^{60} +(-8.26139 + 14.3091i) q^{61} +9.63087i q^{62} +(130.681 + 75.4488i) q^{63} +64.0000 q^{64} -20.8634 q^{65} +(85.8634 + 148.720i) q^{66} +(-83.0109 - 47.9263i) q^{67} +(-10.0911 - 17.4783i) q^{68} -156.249 q^{69} +(-60.7723 + 35.0869i) q^{70} +(12.6594 - 7.30892i) q^{71} +(59.8178 - 103.607i) q^{72} +(-17.4545 - 30.2320i) q^{73} -102.772 q^{74} +63.1804i q^{75} +(9.13665 - 75.4488i) q^{76} +177.022 q^{77} -58.7319i q^{78} +(-68.0911 + 39.3124i) q^{79} +(27.8178 + 48.1819i) q^{80} +(-4.02277 - 6.96765i) q^{81} +(34.9089 + 60.4640i) q^{82} -92.9922i q^{83} +(-98.7723 - 171.079i) q^{84} +(8.77226 - 15.1940i) q^{85} +(18.7723 - 10.8382i) q^{86} -36.5960i q^{87} -140.348i q^{88} +(56.2495 - 97.4270i) q^{89} +104.000 q^{90} +(-52.4317 - 30.2714i) q^{91} +(110.590 + 63.8492i) q^{92} +(-11.7842 - 20.4108i) q^{93} +(-38.3406 - 22.1359i) q^{94} +(60.7723 - 25.9156i) q^{95} +(-135.636 + 78.3093i) q^{96} +(-63.9772 - 110.812i) q^{97} -105.636 q^{98} +(-227.204 - 131.176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9}+O(q^{10}) $ 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9	$ 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9} - 8 q^{10} - 24 q^{12} - 12 q^{13} - 48 q^{15} + 64 q^{16} - 32 q^{17} + 16 q^{18} + 42 q^{19} - 16 q^{20} - 44 q^{21} + 12 q^{23} - 48 q^{24} - 18 q^{25} - 24 q^{26} - 4 q^{29} - 96 q^{30} + 128 q^{32} + 106 q^{33} - 64 q^{34} - 12 q^{35} + 32 q^{36} - 96 q^{37} + 84 q^{38} - 32 q^{40} + 26 q^{41} - 88 q^{42} - 72 q^{43} + 208 q^{45} + 24 q^{46} - 96 q^{48} - 36 q^{49} - 36 q^{50} - 24 q^{51} - 48 q^{52} + 124 q^{53} + 288 q^{55} + 124 q^{57} - 8 q^{58} - 78 q^{59} - 192 q^{60} - 44 q^{61} + 216 q^{63} + 256 q^{64} + 48 q^{65} + 212 q^{66} - 102 q^{67} - 128 q^{68} - 384 q^{69} - 24 q^{70} + 204 q^{71} + 64 q^{72} - 26 q^{73} - 192 q^{74} + 168 q^{76} + 248 q^{77} - 360 q^{79} - 64 q^{80} - 38 q^{81} + 52 q^{82} - 176 q^{84} - 184 q^{85} - 144 q^{86} - 16 q^{89} + 416 q^{90} - 144 q^{91} + 48 q^{92} - 80 q^{93} + 24 q^{95} - 192 q^{96} - 234 q^{97} - 72 q^{98} - 624 q^{99}+O(q^{100}) $ 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9 - 8 * q^10 - 24 * q^12 - 12 * q^13 - 48 * q^15 + 64 * q^16 - 32 * q^17 + 16 * q^18 + 42 * q^19 - 16 * q^20 - 44 * q^21 + 12 * q^23 - 48 * q^24 - 18 * q^25 - 24 * q^26 - 4 * q^29 - 96 * q^30 + 128 * q^32 + 106 * q^33 - 64 * q^34 - 12 * q^35 + 32 * q^36 - 96 * q^37 + 84 * q^38 - 32 * q^40 + 26 * q^41 - 88 * q^42 - 72 * q^43 + 208 * q^45 + 24 * q^46 - 96 * q^48 - 36 * q^49 - 36 * q^50 - 24 * q^51 - 48 * q^52 + 124 * q^53 + 288 * q^55 + 124 * q^57 - 8 * q^58 - 78 * q^59 - 192 * q^60 - 44 * q^61 + 216 * q^63 + 256 * q^64 + 48 * q^65 + 212 * q^66 - 102 * q^67 - 128 * q^68 - 384 * q^69 - 24 * q^70 + 204 * q^71 + 64 * q^72 - 26 * q^73 - 192 * q^74 + 168 * q^76 + 248 * q^77 - 360 * q^79 - 64 * q^80 - 38 * q^81 + 52 * q^82 - 176 * q^84 - 184 * q^85 - 144 * q^86 - 16 * q^89 + 416 * q^90 - 144 * q^91 + 48 * q^92 - 80 * q^93 + 24 * q^95 - 192 * q^96 - 234 * q^97 - 72 * q^98 - 624 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.00000			1.00000
$2$	2.00000			1.00000
$3$	−4.23861	+	2.44716i	−1.41287	+	0.815721i	−0.995658	−	0.0930873i	$-0.970326\pi$
$3$	−4.23861	+	2.44716i	−1.41287	+	0.815721i	−0.417213	+	0.908809i	$0.636993\pi$
$4$	4.00000			1.00000
$5$	1.73861	+	3.01137i	0.347723	+	0.602273i	0.985845	−	0.167662i	$-0.0536218\pi$
$5$	1.73861	+	3.01137i	0.347723	+	0.602273i	−0.638122	+	0.769935i	$0.720288\pi$
$6$	−8.47723	+	4.89433i	−1.41287	+	0.815721i
$7$			10.0905i			1.44150i	0.693197	+	0.720749i	$0.256202\pi$
$7$			10.0905i			1.44150i	−0.693197	+	0.720749i	$0.743798\pi$
$8$	8.00000			1.00000
$9$	7.47723	−	12.9509i	0.830803	−	1.43899i
$10$	3.47723	+	6.02273i	0.347723	+	0.602273i
$11$		−	17.5434i		−	1.59486i	−0.603413	−	0.797429i	$-0.706193\pi$
$11$		−	17.5434i		−	1.59486i	0.603413	−	0.797429i	$-0.293807\pi$
$12$	−16.9545	+	9.78866i	−1.41287	+	0.815721i
$13$	−3.00000	+	5.19615i	−0.230769	+	0.399704i	−0.958035	−	0.286652i	$-0.907458\pi$
$13$	−3.00000	+	5.19615i	−0.230769	+	0.399704i	0.727265	+	0.686356i	$0.240791\pi$
$14$			20.1810i			1.44150i
$15$	−14.7386	−	8.50934i	−0.982574	−	0.567289i
$16$	16.0000			1.00000
$17$	−2.52277	−	4.36957i	−0.148398	−	0.257034i	0.782237	−	0.622981i	$-0.214078\pi$
$17$	−2.52277	−	4.36957i	−0.148398	−	0.257034i	−0.930636	+	0.365947i	$0.880745\pi$
$18$	14.9545	−	25.9019i	0.830803	−	1.43899i
$19$	2.28416	−	18.8622i	0.120219	−	0.992747i
$19$	2.28416	−	18.8622i	0.120219	−	0.992747i
$20$	6.95445	+	12.0455i	0.347723	+	0.602273i
$21$	−24.6931	−	42.7696i	−1.17586	−	2.03665i
$22$		−	35.0869i		−	1.59486i
$23$	27.6475	+	15.9623i	1.20207	+	0.694013i	0.961014	−	0.276499i	$-0.0891743\pi$
$23$	27.6475	+	15.9623i	1.20207	+	0.694013i	0.241052	+	0.970512i	$0.422508\pi$
$24$	−33.9089	+	19.5773i	−1.41287	+	0.815721i
$25$	6.45445	−	11.1794i	0.258178	−	0.447177i
$26$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$27$			29.1430i			1.07937i
$28$			40.3619i			1.44150i
$29$	−3.73861	+	6.47547i	−0.128918	+	0.223292i	−0.923258	−	0.384182i	$-0.874484\pi$
$29$	−3.73861	+	6.47547i	−0.128918	+	0.223292i	0.794340	+	0.607474i	$0.207817\pi$
$30$	−29.4772	−	17.0187i	−0.982574	−	0.567289i
$31$			4.81544i			0.155337i	0.996979	+	0.0776683i	$0.0247475\pi$
$31$			4.81544i			0.155337i	−0.996979	+	0.0776683i	$0.975252\pi$
$32$	32.0000			1.00000
$33$	42.9317	+	74.3598i	1.30096	+	2.25333i
$34$	−5.04555	−	8.73915i	−0.148398	−	0.257034i
$35$	−30.3861	+	17.5434i	−0.868175	+	0.501241i
$36$	29.9089	−	51.8037i	0.830803	−	1.43899i
$37$	−51.3861			−1.38881			−0.694407	−	0.719582i	$-0.744333\pi$
$37$	−51.3861			−1.38881			−0.694407	+	0.719582i	$0.744333\pi$
$38$	4.56832	−	37.7244i	0.120219	−	0.992747i
$39$		−	29.3660i		−	0.752974i
$40$	13.9089	+	24.0909i	0.347723	+	0.602273i
$41$	17.4545	+	30.2320i	0.425718	+	0.737366i	0.996487	−	0.0837450i	$-0.0266881\pi$
$41$	17.4545	+	30.2320i	0.425718	+	0.737366i	−0.570769	+	0.821111i	$0.693355\pi$
$42$	−49.3861	−	85.5393i	−1.17586	−	2.03665i
$43$	9.38613	−	5.41908i	0.218282	−	0.126025i	−0.386872	−	0.922133i	$-0.626445\pi$
$43$	9.38613	−	5.41908i	0.218282	−	0.126025i	0.605155	+	0.796108i	$0.293111\pi$
$44$		−	70.1738i		−	1.59486i
$45$	52.0000			1.15556
$46$	55.2950	+	31.9246i	1.20207	+	0.694013i
$47$	−19.1703	−	11.0680i	−0.407879	−	0.235489i	0.281999	−	0.959415i	$-0.409002\pi$
$47$	−19.1703	−	11.0680i	−0.407879	−	0.235489i	−0.689878	+	0.723926i	$0.742336\pi$
$48$	−67.8178	+	39.1546i	−1.41287	+	0.815721i
$49$	−52.8178			−1.07791
$50$	12.9089	−	22.3589i	0.258178	−	0.447177i
$51$	21.3861	+	12.3473i	0.419336	+	0.242104i
$52$	−12.0000	+	20.7846i	−0.230769	+	0.399704i
$53$	20.0455	−	34.7199i	0.378218	−	0.655093i	−0.612585	−	0.790405i	$-0.709870\pi$
$53$	20.0455	−	34.7199i	0.378218	−	0.655093i	0.990803	+	0.135312i	$0.0432037\pi$
$54$			58.2861i			1.07937i
$55$	52.8297	−	30.5012i	0.960540	−	0.554568i
$56$			80.7238i			1.44150i
$57$	36.4772	+	85.5393i	0.639951	+	1.50069i
$58$	−7.47723	+	12.9509i	−0.128918	+	0.223292i
$59$	−16.7614	+	9.67719i	−0.284091	+	0.164020i	−0.635274	−	0.772287i	$-0.719113\pi$
$59$	−16.7614	+	9.67719i	−0.284091	+	0.164020i	0.351183	+	0.936307i	$0.385780\pi$
$60$	−58.9545	−	34.0374i	−0.982574	−	0.567289i
$61$	−8.26139	+	14.3091i	−0.135433	+	0.234576i	−0.925763	−	0.378105i	$-0.876576\pi$
$61$	−8.26139	+	14.3091i	−0.135433	+	0.234576i	0.790330	+	0.612681i	$0.209909\pi$
$62$			9.63087i			0.155337i
$63$	130.681	+	75.4488i	2.07430	+	1.19760i
$64$	64.0000			1.00000
$65$	−20.8634			−0.320975
$66$	85.8634	+	148.720i	1.30096	+	2.25333i
$67$	−83.0109	−	47.9263i	−1.23897	−	0.715319i	−0.270085	−	0.962837i	$-0.587052\pi$
$67$	−83.0109	−	47.9263i	−1.23897	−	0.715319i	−0.968883	+	0.247518i	$0.920385\pi$
$68$	−10.0911	−	17.4783i	−0.148398	−	0.257034i
$69$	−156.249			−2.26449
$70$	−60.7723	+	35.0869i	−0.868175	+	0.501241i
$71$	12.6594	−	7.30892i	0.178302	−	0.102943i	−0.408193	−	0.912896i	$-0.633841\pi$
$71$	12.6594	−	7.30892i	0.178302	−	0.102943i	0.586495	+	0.809953i	$0.300508\pi$
$72$	59.8178	−	103.607i	0.830803	−	1.43899i
$73$	−17.4545	−	30.2320i	−0.239102	−	0.414137i	0.721355	−	0.692566i	$-0.243520\pi$
$73$	−17.4545	−	30.2320i	−0.239102	−	0.414137i	−0.960457	+	0.278429i	$0.910186\pi$
$74$	−102.772			−1.38881
$75$			63.1804i			0.842405i
$76$	9.13665	−	75.4488i	0.120219	−	0.992747i
$77$	177.022			2.29898
$78$		−	58.7319i		−	0.752974i
$79$	−68.0911	+	39.3124i	−0.861913	+	0.497625i	−0.864652	−	0.502371i	$-0.832461\pi$
$79$	−68.0911	+	39.3124i	−0.861913	+	0.497625i	0.00273968	+	0.999996i	$0.499128\pi$
$80$	27.8178	+	48.1819i	0.347723	+	0.602273i
$81$	−4.02277	−	6.96765i	−0.0496639	−	0.0860204i
$82$	34.9089	+	60.4640i	0.425718	+	0.737366i
$83$		−	92.9922i		−	1.12039i	−0.828361	−	0.560194i	$-0.810726\pi$
$83$		−	92.9922i		−	1.12039i	0.828361	−	0.560194i	$-0.189274\pi$
$84$	−98.7723	−	171.079i	−1.17586	−	2.03665i
$85$	8.77226	−	15.1940i	0.103203	−	0.178753i
$86$	18.7723	−	10.8382i	0.218282	−	0.126025i
$87$		−	36.5960i		−	0.420644i
$88$		−	140.348i		−	1.59486i
$89$	56.2495	−	97.4270i	0.632017	−	1.09468i	−0.355122	−	0.934820i	$-0.615561\pi$
$89$	56.2495	−	97.4270i	0.632017	−	1.09468i	0.987139	−	0.159865i	$-0.0511059\pi$
$90$	104.000			1.15556
$91$	−52.4317	−	30.2714i	−0.576172	−	0.332653i
$92$	110.590	+	63.8492i	1.20207	+	0.694013i
$93$	−11.7842	−	20.4108i	−0.126711	−	0.219471i
$94$	−38.3406	−	22.1359i	−0.407879	−	0.235489i
$95$	60.7723	−	25.9156i	0.639708	−	0.272796i
$96$	−135.636	+	78.3093i	−1.41287	+	0.815721i
$97$	−63.9772	−	110.812i	−0.659559	−	1.14239i	−0.980730	−	0.195368i	$-0.937410\pi$
$97$	−63.9772	−	110.812i	−0.659559	−	1.14239i	0.321171	−	0.947021i	$-0.395924\pi$
$98$	−105.636			−1.07791
$99$	−227.204	−	131.176i	−2.29499	−	1.32501i
$100$	25.8178	−	44.7177i	0.258178	−	0.447177i
$101$	−80.9425	+	140.197i	−0.801411	+	1.38809i	0.117276	+	0.993099i	$0.462584\pi$
$101$	−80.9425	+	140.197i	−0.801411	+	1.38809i	−0.918687	+	0.394986i	$0.870750\pi$
$102$	42.7723	+	24.6946i	0.419336	+	0.242104i
$103$			166.723i			1.61867i	0.587349	+	0.809334i	$0.300172\pi$
$103$			166.723i			1.61867i	−0.587349	+	0.809334i	$0.699828\pi$
$104$	−24.0000	+	41.5692i	−0.230769	+	0.399704i
$105$	85.8634	−	148.720i	0.817746	−	1.41638i
$106$	40.0911	−	69.4398i	0.378218	−	0.655093i
$107$			181.629i			1.69746i	0.528823	+	0.848732i	$0.322633\pi$
$107$			181.629i			1.69746i	−0.528823	+	0.848732i	$0.677367\pi$
$108$			116.572i			1.07937i
$109$	−40.8634	−	70.7774i	−0.374893	−	0.649334i	0.615418	−	0.788201i	$-0.288987\pi$
$109$	−40.8634	−	70.7774i	−0.374893	−	0.649334i	−0.990311	+	0.138867i	$0.955654\pi$
$110$	105.659	−	61.0025i	0.960540	−	0.554568i
$111$	217.806	−	125.750i	1.96222	−	1.13289i
$112$			161.448i			1.44150i
$113$	−27.0911			−0.239744			−0.119872	−	0.992789i	$-0.538248\pi$
$113$	−27.0911			−0.239744			−0.119872	+	0.992789i	$0.538248\pi$
$114$	72.9545	+	171.079i	0.639951	+	1.50069i
$115$			111.009i			0.965296i
$116$	−14.9545	+	25.9019i	−0.128918	+	0.223292i
$117$	44.8634	+	77.7056i	0.383447	+	0.664150i
$118$	−33.5228	+	19.3544i	−0.284091	+	0.164020i
$119$	44.0911	−	25.4560i	0.370513	−	0.213916i
$120$	−117.909	−	68.0747i	−0.982574	−	0.567289i
$121$	−186.772			−1.54357
$122$	−16.5228	+	28.6183i	−0.135433	+	0.234576i
$123$	−147.965	−	85.4278i	−1.20297	−	0.694535i
$124$			19.2617i			0.155337i
$125$	131.818			1.05454
$126$	261.362	+	150.898i	2.07430	+	1.19760i
$127$	−122.204	−	70.5545i	−0.962236	−	0.555547i	−0.0653753	−	0.997861i	$-0.520824\pi$
$127$	−122.204	−	70.5545i	−0.962236	−	0.555547i	−0.896860	+	0.442314i	$0.854158\pi$
$128$	128.000			1.00000
$129$	−26.5228	+	45.9388i	−0.205603	+	0.356115i
$130$	−41.7267			−0.320975
$131$	117.056	−	67.5826i	0.893560	−	0.515897i	0.0184550	−	0.999830i	$-0.494125\pi$
$131$	117.056	−	67.5826i	0.893560	−	0.515897i	0.875105	+	0.483932i	$0.160792\pi$
$132$	171.727	+	297.439i	1.30096	+	2.25333i
$133$	190.329	+	23.0483i	1.43104	+	0.173295i
$134$	−166.022	−	95.8527i	−1.23897	−	0.715319i
$135$	−87.7603	+	50.6685i	−0.650077	+	0.375322i
$136$	−20.1822	−	34.9566i	−0.148398	−	0.257034i
$137$	55.5911	−	96.2866i	0.405774	−	0.702822i	−0.588637	−	0.808398i	$-0.700335\pi$
$137$	55.5911	−	96.2866i	0.405774	−	0.702822i	0.994411	+	0.105576i	$0.0336685\pi$
$138$	−312.499			−2.26449
$139$	−13.7376	−	7.93139i	−0.0988315	−	0.0570604i	0.449770	−	0.893145i	$-0.351506\pi$
$139$	−13.7376	−	7.93139i	−0.0988315	−	0.0570604i	−0.548601	+	0.836084i	$0.684839\pi$
$140$	−121.545	+	70.1738i	−0.868175	+	0.501241i
$141$	108.341			0.768373
$142$	25.3188	−	14.6178i	0.178302	−	0.102943i
$143$	91.1584	+	52.6303i	0.637471	+	0.368044i
$144$	119.636	−	207.215i	0.830803	−	1.43899i
$145$	−26.0000			−0.179310
$146$	−34.9089	−	60.4640i	−0.239102	−	0.414137i
$147$	223.874	−	129.254i	1.52295	−	0.879278i
$148$	−205.545			−1.38881
$149$	19.7842	+	34.2672i	0.132780	+	0.229981i	0.924747	−	0.380582i	$-0.124276\pi$
$149$	19.7842	+	34.2672i	0.132780	+	0.229981i	−0.791967	+	0.610563i	$0.790943\pi$
$150$			126.361i			0.842405i
$151$			4.81544i			0.0318903i	0.999873	+	0.0159452i	$0.00507571\pi$
$151$			4.81544i			0.0318903i	−0.999873	+	0.0159452i	$0.994924\pi$
$152$	18.2733	−	150.898i	0.120219	−	0.992747i
$153$	−75.4534			−0.493160
$154$	354.043			2.29898
$155$	−14.5010	+	8.37218i	−0.0935551	+	0.0540141i
$156$		−	117.464i		−	0.752974i
$157$	−29.0455	−	50.3084i	−0.185003	−	0.320435i	0.758574	−	0.651587i	$-0.225896\pi$
$157$	−29.0455	−	50.3084i	−0.185003	−	0.320435i	−0.943578	+	0.331151i	$0.892563\pi$
$158$	−136.182	+	78.6248i	−0.861913	+	0.497625i
$159$			196.219i			1.23408i
$160$	55.6356	+	96.3637i	0.347723	+	0.602273i
$161$	−161.067	+	278.977i	−1.00042	+	1.73277i
$162$	−8.04555	−	13.9353i	−0.0496639	−	0.0860204i
$163$			207.884i			1.27536i	0.770301	+	0.637680i	$0.220106\pi$
$163$			207.884i			1.27536i	−0.770301	+	0.637680i	$0.779894\pi$
$164$	69.8178	+	120.928i	0.425718	+	0.737366i
$165$	−149.283	+	258.566i	−0.904746	+	1.56707i
$166$		−	185.984i		−	1.12039i
$167$	−103.319	−	59.6512i	−0.618676	−	0.357193i	0.157678	−	0.987491i	$-0.449599\pi$
$167$	−103.319	−	59.6512i	−0.618676	−	0.357193i	−0.776353	+	0.630298i	$0.782933\pi$
$168$	−197.545	−	342.157i	−1.17586	−	2.03665i
$169$	66.5000	+	115.181i	0.393491	+	0.681547i
$170$	17.5445	−	30.3880i	0.103203	−	0.178753i
$171$	−227.204	−	170.619i	−1.32868	−	0.997772i
$172$	37.5445	−	21.6763i	0.218282	−	0.126025i
$173$	48.1366	+	83.3751i	0.278247	+	0.481937i	0.970949	−	0.239286i	$-0.0769135\pi$
$173$	48.1366	+	83.3751i	0.278247	+	0.481937i	−0.692703	+	0.721223i	$0.743580\pi$
$174$		−	73.1920i		−	0.420644i
$175$	112.806	+	65.1285i	0.644605	+	0.372163i
$176$		−	280.695i		−	1.59486i
$177$	47.3634	−	82.0357i	0.267590	−	0.463479i
$178$	112.499	−	194.854i	0.632017	−	1.09468i
$179$			205.366i			1.14730i	0.819101	+	0.573649i	$0.194473\pi$
$179$			205.366i			1.14730i	−0.819101	+	0.573649i	$0.805527\pi$
$180$	208.000			1.15556
$181$	107.943	−	186.962i	0.596368	−	1.03294i	−0.396985	−	0.917825i	$-0.629943\pi$
$181$	107.943	−	186.962i	0.596368	−	1.03294i	0.993352	−	0.115114i	$-0.0367233\pi$
$182$	−104.863	−	60.5429i	−0.576172	−	0.332653i
$183$		−	80.8679i		−	0.441901i
$184$	221.180	+	127.698i	1.20207	+	0.694013i
$185$	−89.3406	−	154.742i	−0.482922	−	0.836446i
$186$	−23.5683	−	40.8215i	−0.126711	−	0.219471i
$187$	−76.6573	+	44.2581i	−0.409932	+	0.236675i
$188$	−76.6812	−	44.2719i	−0.407879	−	0.235489i
$189$	−294.067			−1.55591
$190$	121.545	−	51.8312i	0.639708	−	0.272796i
$191$		−	182.548i		−	0.955748i	−0.878428	−	0.477874i	$-0.841408\pi$
$191$		−	182.548i		−	0.955748i	0.878428	−	0.477874i	$-0.158592\pi$
$192$	−271.271	+	156.619i	−1.41287	+	0.815721i
$193$	50.5228	+	87.5080i	0.261776	+	0.453409i	0.966714	−	0.255860i	$-0.0823585\pi$
$193$	50.5228	+	87.5080i	0.261776	+	0.453409i	−0.704938	+	0.709269i	$0.749025\pi$
$194$	−127.954	−	221.624i	−0.659559	−	1.14239i
$195$	88.4317	−	51.0561i	0.453496	−	0.261826i
$196$	−211.271			−1.07791
$197$	10.1584			0.0515654			0.0257827	−	0.999668i	$-0.491792\pi$
$197$	10.1584			0.0515654			0.0257827	+	0.999668i	$0.491792\pi$
$198$	−454.408	−	262.353i	−2.29499	−	1.32501i
$199$	158.976	+	91.7849i	0.798875	+	0.461231i	0.843078	−	0.537792i	$-0.180741\pi$
$199$	158.976	+	91.7849i	0.798875	+	0.461231i	−0.0442024	+	0.999023i	$0.514075\pi$
$200$	51.6356	−	89.4355i	0.258178	−	0.447177i
$201$	469.135			2.33400
$202$	−161.885	+	280.393i	−0.801411	+	1.38809i
$203$	−65.3406	−	37.7244i	−0.321875	−	0.185834i
$204$	85.5445	+	49.3891i	0.419336	+	0.242104i
$205$	−60.6931	+	105.123i	−0.296064	+	0.512797i
$206$			333.445i			1.61867i
$207$	413.453	−	238.707i	1.99736	−	1.15318i
$208$	−48.0000	+	83.1384i	−0.230769	+	0.399704i
$209$	−330.908	−	40.0721i	−1.58329	−	0.191732i
$210$	171.727	−	297.439i	0.817746	−	1.41638i
$211$	255.226	−	147.355i	1.20960	−	0.698363i	0.246928	−	0.969034i	$-0.420579\pi$
$211$	255.226	−	147.355i	1.20960	−	0.698363i	0.962672	+	0.270671i	$0.0872454\pi$
$212$	80.1822	−	138.880i	0.378218	−	0.655093i
$213$	−35.7723	+	61.9594i	−0.167945	+	0.290889i
$214$			363.257i			1.69746i
$215$	32.6377	+	18.8434i	0.151803	+	0.0876436i
$216$			233.144i			1.07937i
$217$	−48.5901			−0.223917
$218$	−81.7267	−	141.555i	−0.374893	−	0.649334i
$219$	147.965	+	85.4278i	0.675641	+	0.390081i
$220$	211.319	−	122.005i	0.960540	−	0.554568i
$221$	30.2733			0.136983
$222$	435.612	−	251.501i	1.96222	−	1.13289i
$223$	28.9425	−	16.7100i	0.129787	−	0.0749327i	−0.433701	−	0.901057i	$-0.642792\pi$
$223$	28.9425	−	16.7100i	0.129787	−	0.0749327i	0.563488	+	0.826124i	$0.309459\pi$
$224$			322.895i			1.44150i
$225$	−96.5228	−	167.182i	−0.428990	−	0.743033i
$226$	−54.1822			−0.239744
$227$			27.1743i			0.119711i	0.998207	+	0.0598553i	$0.0190639\pi$
$227$			27.1743i			0.119711i	−0.998207	+	0.0598553i	$0.980936\pi$
$228$	145.909	+	342.157i	0.639951	+	1.50069i
$229$	−251.818			−1.09964			−0.549821	−	0.835283i	$-0.685304\pi$
$229$	−251.818			−1.09964			−0.549821	+	0.835283i	$0.685304\pi$
$230$			222.018i			0.965296i
$231$	−750.327	+	433.201i	−3.24817	+	1.87533i
$232$	−29.9089	+	51.8037i	−0.128918	+	0.223292i
$233$	82.2723	+	142.500i	0.353100	+	0.611587i	0.986791	−	0.161999i	$-0.0517943\pi$
$233$	82.2723	+	142.500i	0.353100	+	0.611587i	−0.633691	+	0.773586i	$0.718461\pi$
$234$	89.7267	+	155.411i	0.383447	+	0.664150i
$235$		−	76.9717i		−	0.327539i
$236$	−67.0455	+	38.7088i	−0.284091	+	0.164020i
$237$	192.408	−	333.260i	0.811848	−	1.40616i
$238$	88.1822	−	50.9120i	0.370513	−	0.213916i
$239$		−	119.247i		−	0.498943i	−0.968382	−	0.249471i	$-0.919743\pi$
$239$		−	119.247i		−	0.498943i	0.968382	−	0.249471i	$-0.0802569\pi$
$240$	−235.818	−	136.149i	−0.982574	−	0.567289i
$241$	33.1139	−	57.3549i	0.137402	−	0.237987i	−0.789110	−	0.614251i	$-0.789458\pi$
$241$	33.1139	−	57.3549i	0.137402	−	0.237987i	0.926512	+	0.376264i	$0.122791\pi$
$242$	−373.545			−1.54357
$243$	−193.046	−	111.455i	−0.794426	−	0.458662i
$244$	−33.0455	+	57.2366i	−0.135433	+	0.234576i
$245$	−91.8297	−	159.054i	−0.374815	−	0.649199i
$246$	−295.931	−	170.856i	−1.20297	−	0.694535i
$247$	91.1584	+	68.4555i	0.369062	+	0.277148i
$248$			38.5235i			0.155337i
$249$	227.567	+	394.158i	0.913925	+	1.58296i
$250$	263.636			1.05454
$251$	−161.124	−	93.0248i	−0.641927	−	0.370617i	0.143429	−	0.989661i	$-0.454187\pi$
$251$	−161.124	−	93.0248i	−0.641927	−	0.370617i	−0.785356	+	0.619044i	$0.787520\pi$
$252$	522.725	+	301.795i	2.07430	+	1.19760i
$253$	280.034	−	485.032i	1.10685	−	1.91712i
$254$	−244.408	−	141.109i	−0.962236	−	0.555547i
$255$			85.8686i			0.336740i
$256$	256.000			1.00000
$257$	−151.862	+	263.033i	−0.590904	+	1.02348i	0.403207	+	0.915109i	$0.367895\pi$
$257$	−151.862	+	263.033i	−0.590904	+	1.02348i	−0.994111	+	0.108367i	$0.965438\pi$
$258$	−53.0455	+	91.8776i	−0.205603	+	0.356115i
$259$		−	518.511i		−	2.00197i
$260$	−83.4534			−0.320975
$261$	55.9089	+	96.8371i	0.214210	+	0.371023i
$262$	234.113	−	135.165i	0.893560	−	0.515897i
$263$	75.2376	−	43.4384i	0.286074	−	0.165165i	−0.350096	−	0.936714i	$-0.613851\pi$
$263$	75.2376	−	43.4384i	0.286074	−	0.165165i	0.636170	+	0.771549i	$0.280518\pi$
$264$	343.453	+	594.879i	1.30096	+	2.25333i
$265$	139.406			0.526060
$266$	380.657	+	46.0966i	1.43104	+	0.173295i
$267$			550.607i			2.06220i
$268$	−332.043	−	191.705i	−1.23897	−	0.715319i
$269$	−97.6356	−	169.110i	−0.362958	−	0.628661i	0.625489	−	0.780233i	$-0.284900\pi$
$269$	−97.6356	−	169.110i	−0.362958	−	0.628661i	−0.988446	+	0.151572i	$0.951566\pi$
$270$	−175.521	+	101.337i	−0.650077	+	0.375322i
$271$	−304.010	+	175.520i	−1.12181	+	0.647676i	−0.941862	−	0.336001i	$-0.890926\pi$
$271$	−304.010	+	175.520i	−1.12181	+	0.647676i	−0.179946	+	0.983677i	$0.557592\pi$
$272$	−40.3644	−	69.9132i	−0.148398	−	0.257034i
$273$	296.317			1.08541
$274$	111.182	−	192.573i	0.405774	−	0.702822i
$275$	−196.126	−	113.233i	−0.713185	−	0.411757i
$276$	−624.998			−2.26449
$277$	−115.430			−0.416713			−0.208357	−	0.978053i	$-0.566811\pi$
$277$	−115.430			−0.416713			−0.208357	+	0.978053i	$0.566811\pi$
$278$	−27.4752	−	15.8628i	−0.0988315	−	0.0570604i
$279$	62.3644	+	36.0061i	0.223528	+	0.129054i
$280$	−243.089	+	140.348i	−0.868175	+	0.501241i
$281$	11.9990	−	20.7828i	0.0427009	−	0.0739602i	−0.843885	−	0.536524i	$-0.819737\pi$
$281$	11.9990	−	20.7828i	0.0427009	−	0.0739602i	0.886586	+	0.462564i	$0.153070\pi$
$282$	216.681			0.768373
$283$	−125.237	+	72.3053i	−0.442532	+	0.255496i	−0.704671	−	0.709534i	$-0.748905\pi$
$283$	−125.237	+	72.3053i	−0.442532	+	0.255496i	0.262139	+	0.965030i	$0.415572\pi$
$284$	50.6377	−	29.2357i	0.178302	−	0.102943i
$285$	−194.170	+	258.566i	−0.681299	+	0.907249i
$286$	182.317	+	105.261i	0.637471	+	0.368044i
$287$	−305.055	+	176.124i	−1.06291	+	0.613672i
$288$	239.271	−	414.430i	0.830803	−	1.43899i
$289$	131.771	−	228.234i	0.455956	−	0.789739i
$290$	−52.0000			−0.179310
$291$	542.349	+	313.126i	1.86374	+	1.07603i
$292$	−69.8178	−	120.928i	−0.239102	−	0.414137i
$293$	215.794			0.736498			0.368249	−	0.929727i	$-0.379957\pi$
$293$	215.794			0.736498			0.368249	+	0.929727i	$0.379957\pi$
$294$	447.748	−	258.508i	1.52295	−	0.879278i
$295$	−58.2831	−	33.6498i	−0.197570	−	0.114067i
$296$	−411.089			−1.38881
$297$	511.269			1.72144
$298$	39.5683	+	68.5343i	0.132780	+	0.229981i
$299$	−165.885	+	95.7738i	−0.554800	+	0.320314i
$300$			252.722i			0.842405i
$301$	54.6812	+	94.7105i	0.181665	+	0.314653i
$302$			9.63087i			0.0318903i
$303$		−	792.319i		−	2.61491i
$304$	36.5466	−	301.795i	0.120219	−	0.992747i
$305$	−57.4534			−0.188372
$306$	−150.907			−0.493160
$307$	77.7831	−	44.9081i	0.253365	−	0.146280i	−0.367939	−	0.929850i	$-0.619936\pi$
$307$	77.7831	−	44.9081i	0.253365	−	0.146280i	0.621304	+	0.783569i	$0.286603\pi$
$308$	708.087			2.29898
$309$	−407.998	−	706.673i	−1.32038	−	2.28697i
$310$	−29.0021	+	16.7444i	−0.0935551	+	0.0540141i
$311$		−	345.134i		−	1.10976i	−0.831932	−	0.554878i	$-0.812765\pi$
$311$		−	345.134i		−	1.10976i	0.831932	−	0.554878i	$-0.187235\pi$
$312$		−	234.928i		−	0.752974i
$313$	−261.361	+	452.691i	−0.835020	+	1.44630i	0.0589940	+	0.998258i	$0.481211\pi$
$313$	−261.361	+	452.691i	−0.835020	+	1.44630i	−0.894014	+	0.448039i	$0.852123\pi$
$314$	−58.0911	−	100.617i	−0.185003	−	0.320435i
$315$			524.705i			1.66573i
$316$	−272.364	+	157.250i	−0.861913	+	0.497625i
$317$	−1.54659	+	2.67877i	−0.00487882	+	0.00845037i	−0.868455	−	0.495769i	$-0.834886\pi$
$317$	−1.54659	+	2.67877i	−0.00487882	+	0.00845037i	0.863576	+	0.504219i	$0.168220\pi$
$318$			392.438i			1.23408i
$319$	113.602	+	65.5881i	0.356119	+	0.205605i
$320$	111.271	+	192.727i	0.347723	+	0.602273i
$321$	−444.475	−	769.854i	−1.38466	−	2.39830i
$322$	−322.135	+	557.953i	−1.00042	+	1.73277i
$323$	−88.1822	+	37.6043i	−0.273010	+	0.116422i
$324$	−16.0911	−	27.8706i	−0.0496639	−	0.0860204i
$325$	38.7267	+	67.0766i	0.119159	+	0.206390i
$326$			415.767i			1.27536i
$327$	346.408	+	199.999i	1.05935	+	0.611617i
$328$	139.636	+	241.856i	0.425718	+	0.737366i
$329$	111.681	−	193.437i	0.339456	−	0.587956i
$330$	−298.566	+	517.132i	−0.904746	+	1.56707i
$331$			103.542i			0.312817i	0.987692	+	0.156408i	$0.0499916\pi$
$331$			103.542i			0.312817i	−0.987692	+	0.156408i	$0.950008\pi$
$332$		−	371.969i		−	1.12039i
$333$	−384.226	+	665.498i	−1.15383	+	1.99849i
$334$	−206.638	−	119.302i	−0.618676	−	0.357193i
$335$		−	333.301i		−	0.994930i
$336$	−395.089	−	684.314i	−1.17586	−	2.03665i
$337$	248.203	+	429.900i	0.736507	+	1.27567i	0.954059	+	0.299619i	$0.0968595\pi$
$337$	248.203	+	429.900i	0.736507	+	1.27567i	−0.217552	+	0.976049i	$0.569807\pi$
$338$	133.000	+	230.363i	0.393491	+	0.681547i
$339$	114.829	−	66.2964i	0.338728	−	0.195564i
$340$	35.0890	−	60.7760i	0.103203	−	0.178753i
$341$	84.4793			0.247740
$342$	−454.408	−	341.238i	−1.32868	−	0.997772i
$343$		−	38.5235i		−	0.112313i
$344$	75.0890	−	43.3527i	0.218282	−	0.126025i
$345$	−271.657	−	470.524i	−0.787413	−	1.36384i
$346$	96.2733	+	166.750i	0.278247	+	0.481937i
$347$	484.351	−	279.640i	1.39583	−	0.805880i	0.401873	−	0.915695i	$-0.368359\pi$
$347$	484.351	−	279.640i	1.39583	−	0.805880i	0.993952	+	0.109815i	$0.0350258\pi$
$348$		−	146.384i		−	0.420644i
$349$	−507.271			−1.45350			−0.726750	−	0.686902i	$-0.758970\pi$
$349$	−507.271			−1.45350			−0.726750	+	0.686902i	$0.758970\pi$
$350$	225.612	+	130.257i	0.644605	+	0.372163i
$351$	−151.432	−	87.4291i	−0.431429	−	0.249086i
$352$		−	561.390i		−	1.59486i
$353$	−95.7723			−0.271310			−0.135655	−	0.990756i	$-0.543314\pi$
$353$	−95.7723			−0.271310			−0.135655	+	0.990756i	$0.543314\pi$
$354$	94.7267	−	164.071i	0.267590	−	0.463479i
$355$	44.0197	+	25.4148i	0.123999	+	0.0715909i
$356$	224.998	−	389.708i	0.632017	−	1.09468i
$357$	−124.590	+	215.796i	−0.348992	+	0.604471i
$358$			410.733i			1.14730i
$359$	−185.715	+	107.222i	−0.517311	+	0.298670i	−0.735834	−	0.677162i	$-0.763210\pi$
$359$	−185.715	+	107.222i	−0.517311	+	0.298670i	0.218523	+	0.975832i	$0.429876\pi$
$360$	416.000			1.15556
$361$	−350.565	−	86.1686i	−0.971095	−	0.238694i
$362$	215.885	−	373.924i	0.596368	−	1.03294i
$363$	791.655	−	457.062i	2.18087	−	1.25913i
$364$	−209.727	−	121.086i	−0.576172	−	0.332653i
$365$	60.6931	−	105.123i	0.166282	−	0.288010i
$366$		−	161.736i		−	0.441901i
$367$	−332.602	−	192.028i	−0.906272	−	0.523237i	−0.0270425	−	0.999634i	$-0.508609\pi$
$367$	−332.602	−	192.028i	−0.906272	−	0.523237i	−0.879230	+	0.476398i	$0.841942\pi$
$368$	442.360	+	255.397i	1.20207	+	0.694013i
$369$	522.043			1.41475
$370$	−178.681	−	309.485i	−0.482922	−	0.836446i
$371$	350.341	+	202.269i	0.944314	+	0.545200i
$372$	−47.1366	−	81.6431i	−0.126711	−	0.219471i
$373$	258.091			0.691933			0.345967	−	0.938247i	$-0.387551\pi$
$373$	258.091			0.691933			0.345967	+	0.938247i	$0.387551\pi$
$374$	−153.315	+	88.5163i	−0.409932	+	0.236675i
$375$	−558.725	+	322.580i	−1.48993	+	0.860213i
$376$	−153.362	−	88.5438i	−0.407879	−	0.235489i
$377$	−22.4317	−	38.8528i	−0.0595005	−	0.103058i
$378$	−588.135			−1.55591
$379$		−	118.568i		−	0.312845i	−0.987690	−	0.156423i	$-0.950004\pi$
$379$		−	118.568i		−	0.312845i	0.987690	−	0.156423i	$-0.0499962\pi$
$380$	243.089	−	103.662i	0.639708	−	0.272796i
$381$	690.634			1.81269
$382$		−	365.096i		−	0.955748i
$383$	534.077	−	308.350i	1.39446	−	0.805090i	0.400652	−	0.916230i	$-0.368783\pi$
$383$	534.077	−	308.350i	1.39446	−	0.805090i	0.993805	+	0.111140i	$0.0354502\pi$
$384$	−542.542	+	313.237i	−1.41287	+	0.815721i
$385$	307.772	+	533.077i	0.799408	+	1.38462i
$386$	101.046	+	175.016i	0.261776	+	0.453409i
$387$		−	162.079i		−	0.418808i
$388$	−255.909	−	443.247i	−0.659559	−	1.14239i
$389$	−210.954	+	365.384i	−0.542299	+	0.939290i	0.456472	+	0.889738i	$0.349113\pi$
$389$	−210.954	+	365.384i	−0.542299	+	0.939290i	−0.998772	+	0.0495524i	$0.984221\pi$
$390$	176.863	−	102.112i	0.453496	−	0.261826i
$391$		−	161.077i		−	0.411962i
$392$	−422.542			−1.07791
$393$	−330.771	+	572.913i	−0.841657	+	1.45779i
$394$	20.3168			0.0515654
$395$	−236.768	−	136.698i	−0.599413	−	0.346071i
$396$	−908.816	−	524.705i	−2.29499	−	1.32501i
$397$	264.533	+	458.184i	0.666329	+	1.15412i	0.978923	+	0.204229i	$0.0654687\pi$
$397$	264.533	+	458.184i	0.666329	+	1.15412i	−0.312594	+	0.949887i	$0.601198\pi$
$398$	317.952	+	183.570i	0.798875	+	0.461231i
$399$	−863.132	+	368.073i	−2.16324	+	0.922488i
$400$	103.271	−	178.871i	0.258178	−	0.447177i
$401$	−0.955488	−	1.65495i	−0.00238276	−	0.00412707i	0.864832	−	0.502062i	$-0.167425\pi$
$401$	−0.955488	−	1.65495i	−0.00238276	−	0.00412707i	−0.867214	+	0.497935i	$0.834092\pi$
$402$	938.269			2.33400
$403$	−25.0217	−	14.4463i	−0.0620887	−	0.0358469i
$404$	−323.770	+	560.786i	−0.801411	+	1.38809i
$405$	13.9881	−	24.2281i	0.0345385	−	0.0598224i
$406$	−130.681	−	75.4488i	−0.321875	−	0.185834i
$407$			901.489i			2.21496i
$408$	171.089	+	98.7783i	0.419336	+	0.242104i
$409$	142.932	−	247.565i	0.349466	−	0.605293i	−0.636689	−	0.771121i	$-0.719696\pi$
$409$	142.932	−	247.565i	0.349466	−	0.605293i	0.986155	+	0.165828i	$0.0530296\pi$
$410$	−121.386	+	210.247i	−0.296064	+	0.512797i
$411$			544.162i			1.32400i
$412$			666.891i			1.61867i
$413$	−97.6475	−	169.130i	−0.236435	−	0.409517i
$414$	826.907	−	477.415i	1.99736	−	1.15318i
$415$	280.034	−	161.677i	0.674780	−	0.389584i
$416$	−96.0000	+	166.277i	−0.230769	+	0.399704i
$417$	77.6377			0.186181
$418$	−661.816	−	80.1441i	−1.58329	−	0.191732i
$419$			833.373i			1.98896i	0.104936	+	0.994479i	$0.466536\pi$
$419$			833.373i			1.98896i	−0.104936	+	0.994479i	$0.533464\pi$
$420$	343.453	−	594.879i	0.817746	−	1.41638i
$421$	404.964	+	701.419i	0.961910	+	1.66608i	0.717696	+	0.696356i	$0.245197\pi$
$421$	404.964	+	701.419i	0.961910	+	1.66608i	0.244214	+	0.969721i	$0.421470\pi$
$422$	510.451	−	294.709i	1.20960	−	0.698363i
$423$	−286.681	+	165.515i	−0.677733	+	0.391289i
$424$	160.364	−	277.759i	0.378218	−	0.655093i
$425$	−65.1325			−0.153253
$426$	−71.5445	+	123.919i	−0.167945	+	0.290889i
$427$	−144.386	−	83.3614i	−0.338141	−	0.195226i
$428$			726.515i			1.69746i
$429$	−515.180			−1.20089
$430$	65.2754	+	37.6868i	0.151803	+	0.0876436i
$431$	222.564	+	128.497i	0.516390	+	0.298138i	0.735456	−	0.677572i	$-0.236968\pi$
$431$	222.564	+	128.497i	0.516390	+	0.298138i	−0.219066	+	0.975710i	$0.570301\pi$
$432$			466.289i			1.07937i
$433$	121.137	−	209.815i	0.279761	−	0.484561i	−0.691564	−	0.722315i	$-0.743078\pi$
$433$	121.137	−	209.815i	0.279761	−	0.484561i	0.971325	+	0.237754i	$0.0764113\pi$
$434$	−97.1801			−0.223917
$435$	110.204	−	63.6263i	0.253342	−	0.146267i
$436$	−163.453	−	283.110i	−0.374893	−	0.649334i
$437$	364.236	−	485.032i	0.833491	−	1.10991i
$438$	295.931	+	170.856i	0.675641	+	0.390081i
$439$	−251.216	+	145.040i	−0.572246	+	0.330386i	−0.758046	−	0.652201i	$-0.773846\pi$
$439$	−251.216	+	145.040i	−0.572246	+	0.330386i	0.185800	+	0.982588i	$0.440512\pi$
$440$	422.638	−	244.010i	0.960540	−	0.554568i
$441$	−394.931	+	684.040i	−0.895534	+	1.55111i
$442$	60.5466			0.136983
$443$	187.649	+	108.339i	0.423586	+	0.244557i	0.696610	−	0.717450i	$-0.254691\pi$
$443$	187.649	+	108.339i	0.423586	+	0.244557i	−0.273024	+	0.962007i	$0.588024\pi$
$444$	871.224	−	503.001i	1.96222	−	1.13289i
$445$	391.184			0.879066
$446$	57.8851	−	33.4200i	0.129787	−	0.0749327i
$447$	−167.715	−	96.8302i	−0.375201	−	0.216622i
$448$			645.791i			1.44150i
$449$	−315.820			−0.703385			−0.351693	−	0.936116i	$-0.614394\pi$
$449$	−315.820			−0.703385			−0.351693	+	0.936116i	$0.614394\pi$
$450$	−193.046	−	334.365i	−0.428990	−	0.743033i
$451$	530.373	−	306.211i	1.17599	−	0.678960i
$452$	−108.364			−0.239744
$453$	−11.7842	−	20.4108i	−0.0260136	−	0.0450569i
$454$			54.3486i			0.119711i
$455$		−	210.521i		−	0.462684i
$456$	291.818	+	684.314i	0.639951	+	1.50069i
$457$	−642.996			−1.40699			−0.703497	−	0.710699i	$-0.748379\pi$
$457$	−642.996			−1.40699			−0.703497	+	0.710699i	$0.748379\pi$
$458$	−503.636			−1.09964
$459$	127.343	−	73.5213i	0.277435	−	0.160177i
$460$			444.036i			0.965296i
$461$	109.907	+	190.364i	0.238410	+	0.412938i	0.960258	−	0.279114i	$-0.0900406\pi$
$461$	109.907	+	190.364i	0.238410	+	0.412938i	−0.721848	+	0.692051i	$0.756707\pi$
$462$	−1500.65	+	866.403i	−3.24817	+	1.87533i
$463$		−	66.7372i		−	0.144141i	−0.997400	−	0.0720704i	$-0.977039\pi$
$463$		−	66.7372i		−	0.144141i	0.997400	−	0.0720704i	$-0.0229606\pi$
$464$	−59.8178	+	103.607i	−0.128918	+	0.223292i
$465$	40.9762	−	70.9728i	0.0881208	−	0.152630i
$466$	164.545	+	284.999i	0.353100	+	0.611587i
$467$		−	171.878i		−	0.368046i	−0.982922	−	0.184023i	$-0.941088\pi$
$467$		−	171.878i		−	0.368046i	0.982922	−	0.184023i	$-0.0589121\pi$
$468$	179.453	+	310.822i	0.383447	+	0.664150i
$469$	483.600	−	837.620i	1.03113	−	1.78597i
$470$		−	153.943i		−	0.327539i
$471$	246.226	+	142.158i	0.522772	+	0.301823i
$472$	−134.091	+	77.4175i	−0.284091	+	0.164020i
$473$	−95.0694	−	164.665i	−0.200992	−	0.348129i
$474$	384.816	−	666.520i	0.811848	−	1.40616i
$475$	−196.126	−	147.281i	−0.412896	−	0.310065i
$476$	176.364	−	101.824i	0.370513	−	0.213916i
$477$	−299.770	−	519.217i	−0.628449	−	1.08851i
$478$		−	238.495i		−	0.498943i
$479$	−19.8178	−	11.4418i	−0.0413733	−	0.0238869i	0.479171	−	0.877722i	$-0.340937\pi$
$479$	−19.8178	−	11.4418i	−0.0413733	−	0.0238869i	−0.520544	+	0.853835i	$0.674271\pi$
$480$	−471.636	−	272.299i	−0.982574	−	0.567289i
$481$	154.158	−	267.010i	0.320496	−	0.555115i
$482$	66.2277	−	114.710i	0.137402	−	0.237987i
$483$		−	1576.63i		−	3.26425i
$484$	−747.089			−1.54357
$485$	222.463	−	385.318i	0.458687	−	0.794469i
$486$	−386.091	−	222.910i	−0.794426	−	0.458662i
$487$			146.082i			0.299963i	0.988689	+	0.149982i	$0.0479215\pi$
$487$			146.082i			0.299963i	−0.988689	+	0.149982i	$0.952079\pi$
$488$	−66.0911	+	114.473i	−0.135433	+	0.234576i
$489$	−508.726	−	881.139i	−1.04034	−	1.80192i
$490$	−183.659	−	318.107i	−0.374815	−	0.649199i
$491$	−412.931	+	238.406i	−0.840999	+	0.485551i	−0.857604	−	0.514311i	$-0.828048\pi$
$491$	−412.931	+	238.406i	−0.840999	+	0.485551i	0.0166045	+	0.999862i	$0.494714\pi$
$492$	−591.861	−	341.711i	−1.20297	−	0.694535i
$493$	37.7267			0.0765248
$494$	182.317	+	136.911i	0.369062	+	0.277148i
$495$		−	912.259i		−	1.84295i
$496$			77.0470i			0.155337i
$497$	73.7505	+	127.740i	0.148391	+	0.257021i
$498$	455.135	+	788.316i	0.913925	+	1.58296i
$499$	501.621	−	289.611i	1.00525	−	0.580382i	0.0954538	−	0.995434i	$-0.469570\pi$
$499$	501.621	−	289.611i	1.00525	−	0.580382i	0.909798	+	0.415052i	$0.136236\pi$
$500$	527.271			1.05454
$501$	583.905			1.16548
$502$	−322.247	−	186.050i	−0.641927	−	0.370617i
$503$	−181.830	−	104.979i	−0.361490	−	0.208707i	0.308244	−	0.951307i	$-0.400259\pi$
$503$	−181.830	−	104.979i	−0.361490	−	0.208707i	−0.669734	+	0.742601i	$0.733592\pi$
$504$	1045.45	+	603.590i	2.07430	+	1.19760i
$505$	−562.911			−1.11468
$506$	560.067	−	970.065i	1.10685	−	1.91712i
$507$	−563.736	−	325.473i	−1.11190	−	0.641958i
$508$	−488.816	−	282.218i	−0.962236	−	0.555547i
$509$	70.9545	−	122.897i	0.139400	−	0.241447i	−0.787870	−	0.615842i	$-0.788816\pi$
$509$	70.9545	−	122.897i	0.139400	−	0.241447i	0.927270	+	0.374394i	$0.122149\pi$
$510$			171.737i			0.336740i
$511$	305.055	−	176.124i	0.596977	−	0.344665i
$512$	512.000			1.00000
$513$	549.702	+	66.5674i	1.07154	+	0.129761i
$514$	−303.725	+	526.066i	−0.590904	+	1.02348i
$515$	−502.063	+	289.866i	−0.974880	+	0.562847i
$516$	−106.091	+	183.755i	−0.205603	+	0.356115i
$517$	−194.170	+	336.313i	−0.375571	+	0.650508i
$518$		−	1037.02i		−	2.00197i
$519$	−408.065	−	235.597i	−0.786253	−	0.453943i
$520$	−166.907			−0.320975
$521$	−162.683			−0.312252			−0.156126	−	0.987737i	$-0.549901\pi$
$521$	−162.683			−0.312252			−0.156126	+	0.987737i	$0.549901\pi$
$522$	111.818	+	193.674i	0.214210	+	0.371023i
$523$	531.564	+	306.899i	1.01638	+	0.586804i	0.913052	−	0.407843i	$-0.133719\pi$
$523$	531.564	+	306.899i	1.01638	+	0.586804i	0.103323	+	0.994648i	$0.467052\pi$
$524$	468.226	−	270.330i	0.893560	−	0.515897i
$525$	−637.521			−1.21433
$526$	150.475	−	86.8769i	0.286074	−	0.165165i
$527$	21.0414	−	12.1483i	0.0399268	−	0.0230517i
$528$	686.907	+	1189.76i	1.30096	+	2.25333i
$529$	245.090	+	424.508i	0.463308	+	0.802473i
$530$	278.812			0.526060
$531$			289.434i			0.545074i
$532$	761.315	+	92.1932i	1.43104	+	0.173295i
$533$	−209.453			−0.392971
$534$			1101.21i			2.06220i
$535$	−546.950	+	315.782i	−1.02234	+	0.590247i
$536$	−664.087	−	383.411i	−1.23897	−	0.715319i
$537$	−502.565	−	870.468i	−0.935876	−	1.62098i
$538$	−195.271	−	338.220i	−0.362958	−	0.628661i
$539$			926.606i			1.71912i
$540$	−351.041	+	202.674i	−0.650077	+	0.375322i
$541$	−125.818	+	217.923i	−0.232565	+	0.402815i	−0.958562	−	0.284883i	$-0.908045\pi$
$541$	−125.818	+	217.923i	−0.232565	+	0.402815i	0.725997	+	0.687698i	$0.241379\pi$
$542$	−608.020	+	351.040i	−1.12181	+	0.647676i
$543$			1056.61i			1.94588i
$544$	−80.7288	−	139.826i	−0.148398	−	0.257034i
$545$	142.091	−	246.109i	0.260718	−	0.451576i
$546$	592.634			1.08541
$547$	289.521	+	167.155i	0.529288	+	0.305585i	0.740727	−	0.671807i	$-0.234481\pi$
$547$	289.521	+	167.155i	0.529288	+	0.305585i	−0.211438	+	0.977391i	$0.567815\pi$
$548$	222.364	−	385.146i	0.405774	−	0.702822i
$549$	123.545	+	213.985i	0.225036	+	0.389773i
$550$	−392.252	−	226.467i	−0.713185	−	0.411757i
$551$	113.602	+	85.3095i	0.206174	+	0.154827i
$552$	−1250.00			−2.26449
$553$	−396.681	−	687.072i	−0.717326	−	1.24244i
$554$	−230.859			−0.416713
$555$	757.360	+	437.262i	1.36461	+	0.787860i
$556$	−54.9503	−	31.7256i	−0.0988315	−	0.0570604i
$557$	−303.180	+	525.123i	−0.544309	+	0.942771i	0.454341	+	0.890828i	$0.349875\pi$
$557$	−303.180	+	525.123i	−0.544309	+	0.942771i	−0.998650	+	0.0519430i	$0.983459\pi$
$558$	124.729	+	72.0122i	0.223528	+	0.129054i
$559$			65.0290i			0.116331i
$560$	−486.178	+	280.695i	−0.868175	+	0.501241i
$561$	216.614	−	375.186i	0.386121	−	0.668781i
$562$	23.9979	−	41.5656i	0.0427009	−	0.0739602i
$563$		−	136.112i		−	0.241762i	−0.992667	−	0.120881i	$-0.961428\pi$
$563$		−	136.112i		−	0.241762i	0.992667	−	0.120881i	$-0.0385719\pi$
$564$	433.362			0.768373
$565$	−47.1009	−	81.5812i	−0.0833645	−	0.144392i
$566$	−250.473	+	144.611i	−0.442532	+	0.255496i
$567$	70.3069	−	40.5917i	0.123998	−	0.0715904i
$568$	101.275	−	58.4714i	0.178302	−	0.102943i
$569$	1007.04			1.76984			0.884922	−	0.465739i	$-0.154211\pi$
$569$	1007.04			1.76984			0.884922	+	0.465739i	$0.154211\pi$
$570$	−388.341	+	517.132i	−0.681299	+	0.907249i
$571$		−	433.551i		−	0.759284i	−0.925133	−	0.379642i	$-0.876047\pi$
$571$		−	433.551i		−	0.759284i	0.925133	−	0.379642i	$-0.123953\pi$
$572$	364.634	+	210.521i	0.637471	+	0.368044i
$573$	446.725	+	773.750i	0.779624	+	1.35035i
$574$	−610.111	+	352.248i	−1.06291	+	0.613672i
$575$	356.899	−	206.056i	0.620694	−	0.358358i
$576$	478.542	−	828.860i	0.830803	−	1.43899i
$577$	459.998			0.797223			0.398612	−	0.917120i	$-0.369492\pi$
$577$	459.998			0.797223			0.398612	+	0.917120i	$0.369492\pi$
$578$	263.542	−	456.469i	0.455956	−	0.789739i
$579$	−428.293	−	247.275i	−0.739711	−	0.427073i
$580$	−104.000			−0.179310
$581$	938.336			1.61504
$582$	1084.70	+	626.251i	1.86374	+	1.07603i
$583$	−609.107	−	351.668i	−1.04478	−	0.603204i
$584$	−139.636	−	241.856i	−0.239102	−	0.414137i
$585$	−156.000	+	270.200i	−0.266667	+	0.461880i
$586$	431.588			0.736498
$587$	−805.568	+	465.095i	−1.37235	+	0.792326i	−0.991223	−	0.132198i	$-0.957797\pi$
$587$	−805.568	+	465.095i	−1.37235	+	0.792326i	−0.381125	+	0.924524i	$0.624463\pi$
$588$	895.497	−	517.015i	1.52295	−	0.879278i
$589$	90.8297	+	10.9992i	0.154210	+	0.0186744i
$590$	−116.566	−	67.2996i	−0.197570	−	0.114067i
$591$	−43.0575	+	24.8592i	−0.0728553	+	0.0420630i
$592$	−822.178			−1.38881
$593$	218.181	−	377.901i	0.367928	−	0.637270i	−0.621314	−	0.783562i	$-0.713401\pi$
$593$	218.181	−	377.901i	0.367928	−	0.637270i	0.989241	+	0.146292i	$0.0467340\pi$
$594$	1022.54			1.72144
$595$	153.315	+	88.5163i	0.257672	+	0.148767i
$596$	79.1366	+	137.069i	0.132780	+	0.229981i
$597$	−898.451			−1.50494
$598$	−331.770	+	191.548i	−0.554800	+	0.320314i
$599$	−618.142	−	356.885i	−1.03196	−	0.595801i	−0.114412	−	0.993433i	$-0.536499\pi$
$599$	−618.142	−	356.885i	−1.03196	−	0.595801i	−0.917545	+	0.397633i	$0.869832\pi$
$600$			505.443i			0.842405i
$601$	21.9586			0.0365368			0.0182684	−	0.999833i	$-0.494185\pi$
$601$	21.9586			0.0365368			0.0182684	+	0.999833i	$0.494185\pi$
$602$	109.362	+	189.421i	0.181665	+	0.314653i
$603$	−1241.38	+	716.712i	−2.05868	+	1.18858i
$604$			19.2617i			0.0318903i
$605$	−324.725	−	562.440i	−0.536735	−	0.929652i
$606$		−	1584.64i		−	2.61491i
$607$		−	305.012i		−	0.502492i	−0.967923	−	0.251246i	$-0.919160\pi$
$607$		−	305.012i		−	0.502492i	0.967923	−	0.251246i	$-0.0808403\pi$
$608$	73.0932	−	603.590i	0.120219	−	0.992747i
$609$	369.271			0.606357
$610$	−114.907			−0.188372
$611$	115.022	−	66.4078i	0.188252	−	0.108687i
$612$	−301.814			−0.493160
$613$	499.043	+	864.369i	0.814100	+	1.41006i	0.909972	+	0.414669i	$0.136103\pi$
$613$	499.043	+	864.369i	0.814100	+	1.41006i	−0.0958719	+	0.995394i	$0.530564\pi$
$614$	155.566	−	89.8162i	0.253365	−	0.146280i
$615$		−	594.104i		−	0.966022i
$616$	1416.17			2.29898
$617$	66.0683	−	114.434i	0.107080	−	0.185468i	−0.807506	−	0.589859i	$-0.799183\pi$
$617$	66.0683	−	114.434i	0.107080	−	0.185468i	0.914586	+	0.404391i	$0.132517\pi$
$618$	−815.996	−	1413.35i	−1.32038	−	2.28697i
$619$			432.512i			0.698727i	0.936987	+	0.349363i	$0.113602\pi$
$619$			432.512i			0.698727i	−0.936987	+	0.349363i	$0.886398\pi$
$620$	−58.0041	+	33.4887i	−0.0935551	+	0.0540141i
$621$	−465.190	+	805.733i	−0.749098	+	1.29748i
$622$		−	690.268i		−	1.10976i
$623$	983.085	+	567.584i	1.57799	+	0.911050i
$624$		−	469.856i		−	0.752974i
$625$	67.8188	+	117.466i	0.108510	+	0.187945i
$626$	−522.723	+	905.382i	−0.835020	+	1.44630i
$627$	1500.65	−	639.936i	2.39339	−	1.02063i
$628$	−116.182	−	201.233i	−0.185003	−	0.320435i
$629$	129.636	+	224.535i	0.206098	+	0.356972i
$630$			1049.41i			1.66573i
$631$	592.283	+	341.955i	0.938642	+	0.541925i	0.889534	−	0.456868i	$-0.151029\pi$
$631$	592.283	+	341.955i	0.938642	+	0.541925i	0.0491077	+	0.998793i	$0.484362\pi$
$632$	−544.729	+	314.499i	−0.861913	+	0.497625i
$633$	−721.202	+	1249.16i	−1.13934	+	1.97339i
$634$	−3.09317	+	5.35753i	−0.00487882	+	0.00845037i
$635$		−	490.668i		−	0.772705i
$636$			784.876i			1.23408i
$637$	158.453	−	274.449i	0.248749	−	0.430847i
$638$	227.204	+	131.176i	0.356119	+	0.205605i
$639$		−	218.602i		−	0.342100i
$640$	222.542	+	385.455i	0.347723	+	0.602273i
$641$	197.363	+	341.843i	0.307899	+	0.533297i	0.977903	−	0.209061i	$-0.0670407\pi$
$641$	197.363	+	341.843i	0.307899	+	0.533297i	−0.670003	+	0.742358i	$0.733707\pi$
$642$	−888.950	−	1539.71i	−1.38466	−	2.39830i
$643$	−854.326	+	493.245i	−1.32866	+	0.767100i	−0.985092	−	0.172030i	$-0.944968\pi$
$643$	−854.326	+	493.245i	−1.32866	+	0.767100i	−0.343564	+	0.939129i	$0.611634\pi$
$644$	−644.269	+	1115.91i	−1.00042	+	1.73277i
$645$	−184.451			−0.285971
$646$	−176.364	+	75.2085i	−0.273010	+	0.116422i
$647$		−	1173.93i		−	1.81442i	−0.420674	−	0.907212i	$-0.638206\pi$
$647$		−	1173.93i		−	1.81442i	0.420674	−	0.907212i	$-0.361794\pi$
$648$	−32.1822	−	55.7412i	−0.0496639	−	0.0860204i
$649$	169.771	+	294.052i	0.261589	+	0.453085i
$650$	77.4534	+	134.153i	0.119159	+	0.206390i
$651$	205.954	−	118.908i	0.316366	−	0.182654i
$652$			831.535i			1.27536i
$653$	−847.540			−1.29792			−0.648959	−	0.760823i	$-0.724795\pi$
$653$	−847.540			−1.29792			−0.648959	+	0.760823i	$0.724795\pi$
$654$	692.816	+	399.997i	1.05935	+	0.611617i
$655$	407.032	+	235.000i	0.621422	+	0.358778i
$656$	279.271	+	483.712i	0.425718	+	0.737366i
$657$	−522.043			−0.794587
$658$	223.362	−	386.875i	0.339456	−	0.587956i
$659$	566.364	+	326.991i	0.859430	+	0.496192i	0.863821	−	0.503798i	$-0.168064\pi$
$659$	566.364	+	326.991i	0.859430	+	0.496192i	−0.00439135	+	0.999990i	$0.501398\pi$
$660$	−597.132	+	1034.26i	−0.904746	+	1.56707i
$661$	154.170	−	267.031i	0.233238	−	0.403980i	−0.725521	−	0.688200i	$-0.758401\pi$
$661$	154.170	−	267.031i	0.233238	−	0.403980i	0.958759	+	0.284220i	$0.0917346\pi$
$662$			207.085i			0.312817i
$663$	−128.317	+	74.0837i	−0.193540	+	0.111740i
$664$		−	743.938i		−	1.12039i
$665$	261.501	+	613.221i	0.393235	+	0.922137i
$666$	−768.451	+	1331.00i	−1.15383	+	1.99849i
$667$	−206.727	+	119.354i	−0.309935	+	0.178941i
$668$	−413.275	−	238.605i	−0.618676	−	0.357193i
$669$	−81.7842	+	141.654i	−0.122248	+	0.211740i
$670$		−	666.603i		−	0.994930i
$671$	251.032	+	144.933i	0.374116	+	0.215996i
$672$	−790.178	−	1368.63i	−1.17586	−	2.03665i
$673$	110.273			0.163853			0.0819267	−	0.996638i	$-0.473893\pi$
$673$	110.273			0.163853			0.0819267	+	0.996638i	$0.473893\pi$
$674$	496.406	+	859.800i	0.736507	+	1.27567i
$675$	325.803	+	188.102i	0.482671	+	0.278670i
$676$	266.000	+	460.726i	0.393491	+	0.681547i
$677$	−910.356			−1.34469			−0.672346	−	0.740237i	$-0.734713\pi$
$677$	−910.356			−1.34469			−0.672346	+	0.740237i	$0.734713\pi$
$678$	229.657	−	132.593i	0.338728	−	0.195564i
$679$	1118.14	−	645.561i	1.64675	−	0.950753i
$680$	70.1780	−	121.552i	0.103203	−	0.178753i
$681$	−66.5000	−	115.181i	−0.0976505	−	0.169136i
$682$	168.959			0.247740
$683$		−	289.407i		−	0.423729i	−0.977299	−	0.211864i	$-0.932047\pi$
$683$		−	289.407i		−	0.423729i	0.977299	−	0.211864i	$-0.0679535\pi$
$684$	−908.816	−	682.476i	−1.32868	−	0.997772i
$685$	386.606			0.564388
$686$		−	77.0470i		−	0.112313i
$687$	1067.36	−	616.240i	1.55365	−	0.897001i
$688$	150.178	−	86.7053i	0.218282	−	0.126025i
$689$	120.273	+	208.319i	0.174562	+	0.302350i
$690$	−543.315	−	941.049i	−0.787413	−	1.36384i
$691$			308.668i			0.446698i	0.974739	+	0.223349i	$0.0716990\pi$
$691$			308.668i			0.446698i	−0.974739	+	0.223349i	$0.928301\pi$
$692$	192.547	+	333.500i	0.278247	+	0.481937i
$693$	1323.63	−	2292.60i	1.91000	−	3.30822i
$694$	968.703	−	559.281i	1.39583	−	0.805880i
$695$		−	55.1585i		−	0.0793647i
$696$		−	292.768i		−	0.420644i
$697$	88.0673	−	152.537i	0.126352	−	0.218848i
$698$	−1014.54			−1.45350
$699$	−697.440	−	402.667i	−0.997769	−	0.576062i
$700$	451.224	+	260.514i	0.644605	+	0.372163i
$701$	−606.075	−	1049.75i	−0.864586	−	1.49751i	−0.867457	−	0.497512i	$-0.834247\pi$
$701$	−606.075	−	1049.75i	−0.864586	−	1.49751i	0.00287094	−	0.999996i	$-0.499086\pi$
$702$	−302.863	−	174.858i	−0.431429	−	0.249086i
$703$	−117.374	+	969.255i	−0.166962	+	1.37874i
$704$		−	1122.78i		−	1.59486i
$705$	188.362	+	326.253i	0.267181	+	0.462770i
$706$	−191.545			−0.271310
$707$	−1414.65	−	816.749i	−2.00092	−	1.15523i
$708$	189.453	−	328.143i	0.267590	−	0.463479i
$709$	−457.689	+	792.740i	−0.645541	+	1.11811i	0.338635	+	0.940918i	$0.390035\pi$
$709$	−457.689	+	792.740i	−0.645541	+	1.11811i	−0.984176	+	0.177193i	$0.943298\pi$
$710$	88.0393	+	50.8295i	0.123999	+	0.0715909i
$711$			1175.79i			1.65371i
$712$	449.996	−	779.416i	0.632017	−	1.09468i
$713$	−76.8654	+	133.135i	−0.107806	+	0.186725i
$714$	−249.180	+	431.593i	−0.348992	+	0.604471i
$715$			366.015i			0.511909i
$716$			821.465i			1.14730i
$717$	291.818	+	505.443i	0.406998	+	0.704942i
$718$	−371.430	+	214.445i	−0.517311	+	0.298670i
$719$	391.610	−	226.096i	0.544659	−	0.314459i	−0.202306	−	0.979322i	$-0.564844\pi$
$719$	391.610	−	226.096i	0.544659	−	0.314459i	0.746965	+	0.664863i	$0.231510\pi$
$720$	832.000			1.15556
$721$	−1682.31			−2.33330
$722$	−701.130	−	172.337i	−0.971095	−	0.238694i
$723$			324.140i			0.448327i
$724$	431.770	−	747.848i	0.596368	−	1.03294i
$725$	48.2614	+	83.5912i	0.0665674	+	0.115298i
$726$	1583.31	−	914.125i	2.18087	−	1.25913i
$727$	−1194.95	+	689.905i	−1.64367	+	0.948975i	−0.664161	+	0.747590i	$0.731211\pi$
$727$	−1194.95	+	689.905i	−1.64367	+	0.948975i	−0.979512	+	0.201385i	$0.935456\pi$
$728$	−419.453	−	242.172i	−0.576172	−	0.332653i
$729$	1163.40			1.59589
$730$	121.386	−	210.247i	0.166282	−	0.288010i
$731$	−47.3582	−	27.3423i	−0.0647855	−	0.0374039i
$732$		−	323.472i		−	0.441901i
$733$	694.475			0.947442			0.473721	−	0.880675i	$-0.342910\pi$
$733$	694.475			0.947442			0.473721	+	0.880675i	$0.342910\pi$
$734$	−665.204	−	384.056i	−0.906272	−	0.523237i
$735$	778.461	+	449.445i	1.05913	+	0.611489i
$736$	884.720	+	510.794i	1.20207	+	0.694013i
$737$	−840.793	+	1456.30i	−1.14083	+	1.97598i
$738$	1044.09			1.41475
$739$	699.757	−	404.005i	0.946897	−	0.546692i	0.0547817	−	0.998498i	$-0.482554\pi$
$739$	699.757	−	404.005i	0.946897	−	0.546692i	0.892116	+	0.451807i	$0.149220\pi$
$740$	−357.362	−	618.970i	−0.482922	−	0.836446i
$741$	−553.907	−	67.0766i	−0.747513	−	0.0905218i
$742$	700.681	+	404.538i	0.944314	+	0.545200i
$743$	348.962	−	201.473i	0.469666	−	0.271162i	−0.246434	−	0.969160i	$-0.579259\pi$
$743$	348.962	−	201.473i	0.469666	−	0.271162i	0.716100	+	0.697998i	$0.245925\pi$
$744$	−94.2733	−	163.286i	−0.126711	−	0.219471i
$745$	−68.7940	+	119.155i	−0.0923409	+	0.159939i
$746$	516.182			0.691933
$747$	−1204.34	−	695.324i	−1.61223	−	0.930822i
$748$	−306.629	+	177.033i	−0.409932	+	0.236675i
$749$	−1832.72			−2.44689
$750$	−1117.45	+	645.160i	−1.48993	+	0.860213i
$751$	−1181.79	−	682.308i	−1.57362	−	0.908532i	−0.995719	−	0.0924285i	$-0.970537\pi$
$751$	−1181.79	−	682.308i	−1.57362	−	0.908532i	−0.577905	−	0.816104i	$-0.696130\pi$
$752$	−306.725	−	177.088i	−0.407879	−	0.235489i
$753$	910.588			1.20928
$754$	−44.8634	−	77.7056i	−0.0595005	−	0.103058i
$755$	−14.5010	+	8.37218i	−0.0192067	+	0.0110890i
$756$	−1176.27			−1.55591
$757$	−555.043	−	961.363i	−0.733215	−	1.26996i	−0.955502	−	0.294984i	$-0.904686\pi$
$757$	−555.043	−	961.363i	−0.733215	−	1.26996i	0.222288	−	0.974981i	$-0.428648\pi$
$758$		−	237.137i		−	0.312845i
$759$			2741.15i			3.61153i
$760$	486.178	−	207.325i	0.639708	−	0.272796i
$761$	1268.49			1.66688			0.833438	−	0.552613i	$-0.186369\pi$
$761$	1268.49			1.66688			0.833438	+	0.552613i	$0.186369\pi$
$762$	1381.27			1.81269
$763$	714.178	−	412.331i	0.936013	−	0.540407i
$764$		−	730.192i		−	0.955748i
$765$	−131.184	−	227.218i	−0.171483	−	0.297017i
$766$	1068.15	−	616.699i	1.39446	−	0.805090i
$767$		−	116.126i		−	0.151403i
$768$	−1085.08	+	626.474i	−1.41287	+	0.815721i
$769$	542.816	−	940.184i	0.705872	−	1.22261i	−0.260504	−	0.965473i	$-0.583889\pi$
$769$	542.816	−	940.184i	0.705872	−	1.22261i	0.966376	−	0.257134i	$-0.0827781\pi$
$770$	615.545	+	1066.15i	0.799408	+	1.38462i
$771$		−	1486.53i		−	1.92805i
$772$	202.091	+	350.032i	0.261776	+	0.453409i
$773$	489.667	−	848.128i	0.633463	−	1.09719i	−0.353375	−	0.935482i	$-0.614966\pi$
$773$	489.667	−	848.128i	0.633463	−	1.09719i	0.986838	−	0.161709i	$-0.0517006\pi$
$774$		−	324.158i		−	0.418808i
$775$	53.8339	+	31.0810i	0.0694630	+	0.0401045i
$776$	−511.818	−	886.494i	−0.659559	−	1.14239i
$777$	1268.88	+	2197.77i	1.63305	+	2.82853i
$778$	−421.909	+	730.768i	−0.542299	+	0.939290i
$779$	610.111	−	260.175i	0.783197	−	0.333985i
$780$	353.727	−	204.224i	0.453496	−	0.261826i
$781$	−128.224	−	222.090i	−0.164179	−	0.284366i
$782$		−	322.154i		−	0.411962i
$783$	−188.715	−	108.955i	−0.241015	−	0.139150i
$784$	−845.085			−1.07791
$785$	100.998	−	174.934i	0.128660	−	0.222845i
$786$	−661.542	+	1145.83i	−0.841657	+	1.45779i
$787$		−	92.7520i		−	0.117855i	−0.998262	−	0.0589276i	$-0.981232\pi$
$787$		−	92.7520i		−	0.117855i	0.998262	−	0.0589276i	$-0.0187681\pi$
$788$	40.6335			0.0515654
$789$	−212.602	+	368.237i	−0.269457	+	0.466714i
$790$	−473.536	−	273.396i	−0.599413	−	0.346071i
$791$		−	273.362i		−	0.345591i
$792$	−1817.63	−	1049.41i	−2.29499	−	1.32501i
$793$	−49.5683	−	85.8549i	−0.0625073	−	0.108266i
$794$	529.065	+	916.368i	0.666329	+	1.15412i
$795$	−590.887	+	341.149i	−0.743254	+	0.429118i
$796$	635.905	+	367.140i	0.798875	+	0.461231i
$797$	1276.61			1.60176			0.800882	−	0.598822i	$-0.204365\pi$
$797$	1276.61			1.60176			0.800882	+	0.598822i	$0.204365\pi$
$798$	−1726.26	+	736.145i	−2.16324	+	0.922488i
$799$			111.688i			0.139785i
$800$	206.542	−	357.742i	0.258178	−	0.447177i
$801$	−841.180	−	1456.97i	−1.05016	−	1.81893i
$802$	−1.91098	−	3.30991i	−0.00238276	−	0.00412707i
$803$	−530.373	+	306.211i	−0.660490	+	0.381334i
$804$	1876.54			2.33400
$805$	−1120.13			−1.39147
$806$	−50.0435	−	28.8926i	−0.0620887	−	0.0358469i
$807$	827.679	+	477.861i	1.02562	+	0.592145i
$808$	−647.540	+	1121.57i	−0.801411	+	1.38809i
$809$	−1144.13			−1.41425			−0.707125	−	0.707089i	$-0.750008\pi$
$809$	−1144.13			−1.41425			−0.707125	+	0.707089i	$0.750008\pi$
$810$	27.9762	−	48.4562i	0.0345385	−	0.0598224i
$811$	−908.471	−	524.506i	−1.12019	−	0.646740i	−0.178738	−	0.983897i	$-0.557201\pi$
$811$	−908.471	−	524.506i	−1.12019	−	0.646740i	−0.941448	+	0.337157i	$0.890535\pi$
$812$	−261.362	−	150.898i	−0.321875	−	0.185834i
$813$	859.053	−	1487.92i	1.05665	−	1.83016i
$814$			1802.98i			2.21496i
$815$	−626.014	+	361.429i	−0.768115	+	0.443472i
$816$	342.178	+	197.557i	0.419336	+	0.242104i
$817$	−80.7764	−	189.421i	−0.0988695	−	0.231850i
$818$	285.863	−	495.130i	0.349466	−	0.605293i
$819$	−784.087	+	452.693i	−0.957371	+	0.552738i
$820$	−242.772	+	420.494i	−0.296064	+	0.512797i
$821$	−200.770	+	347.744i	−0.244543	+	0.423562i	−0.962003	−	0.273038i	$-0.911971\pi$
$821$	−200.770	+	347.744i	−0.244543	+	0.423562i	0.717460	+	0.696600i	$0.245305\pi$
$822$			1088.32i			1.32400i
$823$	243.748	+	140.728i	0.296171	+	0.170994i	0.640721	−	0.767774i	$-0.278635\pi$
$823$	243.748	+	140.728i	0.296171	+	0.170994i	−0.344551	+	0.938768i	$0.611969\pi$
$824$			1333.78i			1.61867i
$825$	1108.40			1.34352
$826$	−195.295	−	338.261i	−0.236435	−	0.409517i
$827$	551.534	+	318.428i	0.666909	+	0.385040i	0.794904	−	0.606735i	$-0.207521\pi$
$827$	551.534	+	318.428i	0.666909	+	0.385040i	−0.127995	+	0.991775i	$0.540854\pi$
$828$	1653.81	−	954.830i	1.99736	−	1.15318i
$829$	−52.2774			−0.0630608			−0.0315304	−	0.999503i	$-0.510038\pi$
$829$	−52.2774			−0.0630608			−0.0315304	+	0.999503i	$0.510038\pi$
$830$	560.067	−	323.355i	0.674780	−	0.389584i
$831$	489.261	−	282.475i	0.588762	−	0.339922i
$832$	−192.000	+	332.554i	−0.230769	+	0.399704i
$833$	133.247	+	230.791i	0.159961	+	0.277060i
$834$	155.275			0.186181
$835$		−	414.841i		−	0.496816i
$836$	−1323.63	−	160.288i	−1.58329	−	0.191732i
$837$	−140.336			−0.167666
$838$			1666.75i			1.98896i
$839$	934.461	−	539.511i	1.11378	−	0.643041i	0.173974	−	0.984750i	$-0.444339\pi$
$839$	934.461	−	539.511i	1.11378	−	0.643041i	0.939806	+	0.341709i	$0.111006\pi$
$840$	686.907	−	1189.76i	0.817746	−	1.41638i
$841$	392.546	+	679.909i	0.466760	+	0.808453i
$842$	809.929	+	1402.84i	0.961910	+	1.66608i
$843$			117.454i			0.139328i
$844$	1020.90	−	589.418i	1.20960	−	0.698363i
$845$	−231.236	+	400.512i	−0.273651	+	0.473978i
$846$	−573.362	+	331.031i	−0.677733	+	0.391289i
$847$		−	1884.62i		−	2.22506i
$848$	320.729	−	555.519i	0.378218	−	0.655093i
$849$	353.886	−	612.949i	0.416827	−	0.721966i
$850$	−130.265			−0.153253
$851$	−1420.70	−	820.241i	−1.66945	−	0.963855i
$852$	−143.089	+	247.837i	−0.167945	+	0.290889i
$853$	120.683	+	209.029i	0.141481	+	0.245052i	0.928055	−	0.372444i	$-0.121480\pi$
$853$	120.683	+	209.029i	0.141481	+	0.245052i	−0.786574	+	0.617497i	$0.788147\pi$
$854$	−288.772	−	166.723i	−0.338141	−	0.195226i
$855$	118.776	−	980.834i	0.138920	−	1.14717i
$856$			1453.03i			1.69746i
$857$	−282.045	−	488.515i	−0.329107	−	0.570030i	0.653228	−	0.757161i	$-0.273414\pi$
$857$	−282.045	−	488.515i	−0.329107	−	0.570030i	−0.982335	+	0.187132i	$0.940081\pi$
$858$	−1030.36			−1.20089
$859$	794.551	+	458.734i	0.924972	+	0.534033i	0.885218	−	0.465176i	$-0.154009\pi$
$859$	794.551	+	458.734i	0.924972	+	0.534033i	0.0397544	+	0.999209i	$0.487342\pi$
$860$	130.551	+	75.3735i	0.151803	+	0.0876436i
$861$	862.008	−	1493.04i	1.00117	−	1.73408i
$862$	445.128	+	256.995i	0.516390	+	0.298138i
$863$		−	467.620i		−	0.541854i	−0.962600	−	0.270927i	$-0.912670\pi$
$863$		−	467.620i		−	0.541854i	0.962600	−	0.270927i	$-0.0873301\pi$
$864$			932.577i			1.07937i
$865$	−167.382	+	289.914i	−0.193505	+	0.335161i
$866$	242.273	−	419.630i	0.279761	−	0.484561i
$867$			1289.86i			1.48773i
$868$	−194.360			−0.223917
$869$	689.675	+	1194.55i	0.793642	+	1.37463i
$870$	220.408	−	127.253i	0.253342	−	0.146267i
$871$	498.065	−	287.558i	0.571831	−	0.330147i
$872$	−326.907	−	566.219i	−0.374893	−	0.649334i
$873$	−1913.49			−2.19185
$874$	728.471	−	970.065i	0.833491	−	1.10991i
$875$			1330.11i			1.52012i
$876$	591.861	+	341.711i	0.675641	+	0.390081i
$877$	−753.758	−	1305.55i	−0.859474	−	1.48865i	−0.872432	−	0.488736i	$-0.837458\pi$
$877$	−753.758	−	1305.55i	−0.859474	−	1.48865i	0.0129583	−	0.999916i	$-0.495875\pi$
$878$	−502.432	+	290.079i	−0.572246	+	0.330386i
$879$	−914.667	+	528.083i	−1.04058	+	0.600777i
$880$	845.275	−	488.020i	0.960540	−	0.554568i
$881$	−279.998			−0.317818			−0.158909	−	0.987293i	$-0.550798\pi$
$881$	−279.998			−0.317818			−0.158909	+	0.987293i	$0.550798\pi$
$882$	−789.861	+	1368.08i	−0.895534	+	1.55111i
$883$	−305.052	−	176.122i	−0.345473	−	0.199459i	0.317217	−	0.948353i	$-0.397252\pi$
$883$	−305.052	−	176.122i	−0.345473	−	0.199459i	−0.662689	+	0.748894i	$0.730585\pi$
$884$	121.093			0.136983
$885$	329.386			0.372188
$886$	375.297	+	216.678i	0.423586	+	0.244557i
$887$	79.7702	+	46.0553i	0.0899326	+	0.0519226i	0.544292	−	0.838896i	$-0.316798\pi$
$887$	79.7702	+	46.0553i	0.0899326	+	0.0519226i	−0.454359	+	0.890819i	$0.650132\pi$
$888$	1742.45	−	1006.00i	1.96222	−	1.13289i
$889$	711.929	−	1233.10i	0.800820	−	1.38706i
$890$	782.369			0.879066
$891$	−122.237	+	70.5733i	−0.137190	+	0.0792068i
$892$	115.770	−	66.8399i	0.129787	−	0.0749327i
$893$	−252.554	+	336.313i	−0.282816	+	0.376610i
$894$	−335.430	−	193.660i	−0.375201	−	0.216622i
$895$	−618.433	+	357.053i	−0.690987	+	0.398941i
$896$			1291.58i			1.44150i
$897$	468.748	−	811.896i	0.522574	−	0.905124i
$898$	−631.640			−0.703385
$899$	−31.1822	−	18.0030i	−0.0346854	−	0.0200256i
$900$	−386.091	−	668.729i	−0.428990	−	0.743033i
$901$	−202.282			−0.224508
$902$	1060.75	−	612.422i	1.17599	−	0.678960i
$903$	−463.545	−	267.628i	−0.513338	−	0.296376i
$904$	−216.729			−0.239744
$905$	750.681			0.829482
$906$	−23.5683	−	40.8215i	−0.0260136	−	0.0450569i
$907$	−1071.41	+	618.580i	−1.18127	+	0.682007i	−0.956308	−	0.292360i	$-0.905559\pi$
$907$	−1071.41	+	618.580i	−1.18127	+	0.682007i	−0.224962	+	0.974367i	$0.572226\pi$
$908$			108.697i			0.119711i
$909$	1210.45	+	2096.56i	1.33163	+	2.30645i
$910$		−	421.043i		−	0.462684i
$911$		−	391.450i		−	0.429693i	−0.976648	−	0.214846i	$-0.931075\pi$
$911$		−	391.450i		−	0.429693i	0.976648	−	0.214846i	$-0.0689251\pi$
$912$	583.636	+	1368.63i	0.639951	+	1.50069i
$913$	−1631.40			−1.78686
$914$	−1285.99			−1.40699
$915$	243.523	−	140.598i	0.266145	−	0.153659i
$916$	−1007.27			−1.09964
$917$	681.940	+	1181.16i	0.743665	+	1.28806i
$918$	254.685	−	147.043i	0.277435	−	0.160177i
$919$			166.723i			0.181418i	0.995877	+	0.0907088i	$0.0289132\pi$
$919$			166.723i			0.181418i	−0.995877	+	0.0907088i	$0.971087\pi$
$920$			888.072i			0.965296i
$921$	−219.795	+	380.696i	−0.238648	+	0.413351i
$922$	219.814	+	380.728i	0.238410	+	0.412938i
$923$			87.7070i			0.0950239i
$924$	−3001.31	+	1732.81i	−3.24817	+	1.87533i
$925$	−331.669	+	574.468i	−0.358561	+	0.621046i
$926$		−	133.474i		−	0.144141i
$927$	2159.22	+	1246.62i	2.32925	+	1.34479i
$928$	−119.636	+	207.215i	−0.128918	+	0.223292i
$929$	−99.9969	−	173.200i	−0.107639	−	0.186437i	0.807174	−	0.590313i	$-0.200996\pi$
$929$	−99.9969	−	173.200i	−0.107639	−	0.186437i	−0.914813	+	0.403877i	$0.867662\pi$
$930$	81.9524	−	141.946i	0.0881208	−	0.152630i
$931$	−120.644	+	996.260i	−0.129586	+	1.07010i
$932$	329.089	+	569.999i	0.353100	+	0.611587i
$933$	844.600	+	1462.89i	0.905252	+	1.56794i
$934$		−	343.755i		−	0.368046i
$935$	−266.555	−	153.896i	−0.285085	−	0.164594i
$936$	358.907	+	621.645i	0.383447	+	0.664150i
$937$	526.676	−	912.230i	0.562087	−	0.973564i	−0.435227	−	0.900321i	$-0.643332\pi$
$937$	526.676	−	912.230i	0.562087	−	0.973564i	0.997314	−	0.0732431i	$-0.0233349\pi$
$938$	967.200	−	1675.24i	1.03113	−	1.78597i
$939$		−	2558.38i		−	2.72457i
$940$		−	307.887i		−	0.327539i
$941$	18.6356	−	32.2778i	0.0198040	−	0.0343016i	−0.855954	−	0.517053i	$-0.827029\pi$
$941$	18.6356	−	32.2778i	0.0198040	−	0.0343016i	0.875758	+	0.482751i	$0.160362\pi$
$942$	492.451	+	284.317i	0.522772	+	0.301823i
$943$			1114.45i			1.18182i
$944$	−268.182	+	154.835i	−0.284091	+	0.164020i
$945$	−511.269	−	885.544i	−0.541026	−	0.937084i
$946$	−190.139	−	329.330i	−0.200992	−	0.348129i
$947$	−66.9503	+	38.6538i	−0.0706973	+	0.0408171i	−0.534932	−	0.844895i	$-0.679663\pi$
$947$	−66.9503	+	38.6538i	−0.0706973	+	0.0408171i	0.464235	+	0.885712i	$0.346329\pi$
$948$	769.631	−	1333.04i	0.811848	−	1.40616i
$949$	209.453			0.220710
$950$	−392.252	−	294.562i	−0.412896	−	0.310065i
$951$		−	15.1390i		−	0.0159190i
$952$	352.729	−	203.648i	0.370513	−	0.213916i
$953$	−561.682	−	972.862i	−0.589383	−	1.02084i	−0.994313	−	0.106494i	$-0.966037\pi$
$953$	−561.682	−	972.862i	−0.589383	−	1.02084i	0.404930	−	0.914348i	$-0.367296\pi$
$954$	−599.540	−	1038.43i	−0.628449	−	1.08851i
$955$	549.718	−	317.380i	0.575621	−	0.332335i
$956$		−	476.989i		−	0.498943i
$957$	−642.020			−0.670867
$958$	−39.6356	−	22.8836i	−0.0413733	−	0.0238869i
$959$	971.578	+	560.941i	1.01312	+	0.584923i
$960$	−943.271	−	544.598i	−0.982574	−	0.567289i
$961$	937.812			0.975871
$962$	308.317	−	534.020i	0.320496	−	0.555115i
$963$	2352.26	+	1358.08i	2.44264	+	1.41026i
$964$	132.455	−	229.420i	0.137402	−	0.237987i
$965$	−175.679	+	304.285i	−0.182051	+	0.315321i
$966$		−	3153.26i		−	3.26425i
$967$	−1025.02	+	591.795i	−1.06000	+	0.611991i	−0.925432	−	0.378913i	$-0.876298\pi$
$967$	−1025.02	+	591.795i	−1.06000	+	0.611991i	−0.134567	+	0.990904i	$0.542965\pi$
$968$	−1494.18			−1.54357
$969$	281.746	−	375.186i	0.290760	−	0.387189i
$970$	444.926	−	770.635i	0.458687	−	0.794469i
$971$	625.708	−	361.252i	0.644395	−	0.372042i	−0.141911	−	0.989879i	$-0.545325\pi$
$971$	625.708	−	361.252i	0.644395	−	0.372042i	0.786306	+	0.617838i	$0.211991\pi$
$972$	−772.182	−	445.820i	−0.794426	−	0.458662i
$973$	80.0316	−	138.619i	0.0822524	−	0.142465i
$974$			292.164i			0.299963i
$975$	−328.295	−	189.541i	−0.336713	−	0.194401i
$976$	−132.182	+	228.946i	−0.135433	+	0.234576i
$977$	−1305.31			−1.33604			−0.668021	−	0.744143i	$-0.732858\pi$
$977$	−1305.31			−1.33604			−0.668021	+	0.744143i	$0.732858\pi$
$978$	−1017.45	−	1762.28i	−1.04034	−	1.80192i
$979$	−1709.20	−	986.809i	−1.74587	−	1.00798i
$980$	−367.319	−	636.215i	−0.374815	−	0.649199i
$981$	−1222.18			−1.24585
$982$	−825.861	+	476.811i	−0.840999	+	0.485551i
$983$	857.727	−	495.209i	0.872560	−	0.503773i	0.00436204	−	0.999990i	$-0.498612\pi$
$983$	857.727	−	495.209i	0.872560	−	0.503773i	0.868198	+	0.496218i	$0.165278\pi$
$984$	−1183.72	−	683.423i	−1.20297	−	0.694535i
$985$	17.6615	+	30.5906i	0.0179305	+	0.0310565i
$986$	75.4534			0.0765248
$987$			1093.21i			1.10761i
$988$	364.634	+	273.822i	0.369062	+	0.277148i
$989$	346.004			0.349853
$990$		−	1824.52i		−	1.84295i
$991$	−974.899	+	562.858i	−0.983752	+	0.567970i	−0.903401	−	0.428797i	$-0.858938\pi$
$991$	−974.899	+	562.858i	−0.983752	+	0.567970i	−0.0803514	+	0.996767i	$0.525604\pi$
$992$			154.094i			0.155337i
$993$	−253.385	−	438.876i	−0.255171	−	0.441970i
$994$	147.501	+	255.479i	0.148391	+	0.257021i
$995$			638.314i			0.641522i
$996$	910.269	+	1576.63i	0.913925	+	1.58296i
$997$	−639.734	+	1108.05i	−0.641659	+	1.11139i	0.343403	+	0.939188i	$0.388420\pi$
$997$	−639.734	+	1108.05i	−0.641659	+	1.11139i	−0.985062	+	0.172199i	$0.944913\pi$
$998$	1003.24	−	579.222i	1.00525	−	0.580382i
$999$		−	1497.55i		−	1.49905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.g.b.7.1	yes	4
4.3	odd	2		76.3.g.a.7.2	✓	4
19.11	even	3		76.3.g.a.11.2	yes	4
76.11	odd	6	inner	76.3.g.b.11.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.g.a.7.2	✓	4	4.3	odd	2
76.3.g.a.11.2	yes	4	19.11	even	3
76.3.g.b.7.1	yes	4	1.1	even	1	trivial
76.3.g.b.11.1	yes	4	76.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.g (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-4.23861 + 2.44716i) q^{3} +4.00000 q^{4} +(1.73861 + 3.01137i) q^{5} +(-8.47723 + 4.89433i) q^{6} +10.0905i q^{7} +8.00000 q^{8} +(7.47723 - 12.9509i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-4.23861 + 2.44716i) q^{3} +4.00000 q^{4} +(1.73861 + 3.01137i) q^{5} +(-8.47723 + 4.89433i) q^{6} +10.0905i q^{7} +8.00000 q^{8} +(7.47723 - 12.9509i) q^{9} +(3.47723 + 6.02273i) q^{10} -17.5434i q^{11} +(-16.9545 + 9.78866i) q^{12} +(-3.00000 + 5.19615i) q^{13} +20.1810i q^{14} +(-14.7386 - 8.50934i) q^{15} +16.0000 q^{16} +(-2.52277 - 4.36957i) q^{17} +(14.9545 - 25.9019i) q^{18} +(2.28416 - 18.8622i) q^{19} +(6.95445 + 12.0455i) q^{20} +(-24.6931 - 42.7696i) q^{21} -35.0869i q^{22} +(27.6475 + 15.9623i) q^{23} +(-33.9089 + 19.5773i) q^{24} +(6.45445 - 11.1794i) q^{25} +(-6.00000 + 10.3923i) q^{26} +29.1430i q^{27} +40.3619i q^{28} +(-3.73861 + 6.47547i) q^{29} +(-29.4772 - 17.0187i) q^{30} +4.81544i q^{31} +32.0000 q^{32} +(42.9317 + 74.3598i) q^{33} +(-5.04555 - 8.73915i) q^{34} +(-30.3861 + 17.5434i) q^{35} +(29.9089 - 51.8037i) q^{36} -51.3861 q^{37} +(4.56832 - 37.7244i) q^{38} -29.3660i q^{39} +(13.9089 + 24.0909i) q^{40} +(17.4545 + 30.2320i) q^{41} +(-49.3861 - 85.5393i) q^{42} +(9.38613 - 5.41908i) q^{43} -70.1738i q^{44} +52.0000 q^{45} +(55.2950 + 31.9246i) q^{46} +(-19.1703 - 11.0680i) q^{47} +(-67.8178 + 39.1546i) q^{48} -52.8178 q^{49} +(12.9089 - 22.3589i) q^{50} +(21.3861 + 12.3473i) q^{51} +(-12.0000 + 20.7846i) q^{52} +(20.0455 - 34.7199i) q^{53} +58.2861i q^{54} +(52.8297 - 30.5012i) q^{55} +80.7238i q^{56} +(36.4772 + 85.5393i) q^{57} +(-7.47723 + 12.9509i) q^{58} +(-16.7614 + 9.67719i) q^{59} +(-58.9545 - 34.0374i) q^{60} +(-8.26139 + 14.3091i) q^{61} +9.63087i q^{62} +(130.681 + 75.4488i) q^{63} +64.0000 q^{64} -20.8634 q^{65} +(85.8634 + 148.720i) q^{66} +(-83.0109 - 47.9263i) q^{67} +(-10.0911 - 17.4783i) q^{68} -156.249 q^{69} +(-60.7723 + 35.0869i) q^{70} +(12.6594 - 7.30892i) q^{71} +(59.8178 - 103.607i) q^{72} +(-17.4545 - 30.2320i) q^{73} -102.772 q^{74} +63.1804i q^{75} +(9.13665 - 75.4488i) q^{76} +177.022 q^{77} -58.7319i q^{78} +(-68.0911 + 39.3124i) q^{79} +(27.8178 + 48.1819i) q^{80} +(-4.02277 - 6.96765i) q^{81} +(34.9089 + 60.4640i) q^{82} -92.9922i q^{83} +(-98.7723 - 171.079i) q^{84} +(8.77226 - 15.1940i) q^{85} +(18.7723 - 10.8382i) q^{86} -36.5960i q^{87} -140.348i q^{88} +(56.2495 - 97.4270i) q^{89} +104.000 q^{90} +(-52.4317 - 30.2714i) q^{91} +(110.590 + 63.8492i) q^{92} +(-11.7842 - 20.4108i) q^{93} +(-38.3406 - 22.1359i) q^{94} +(60.7723 - 25.9156i) q^{95} +(-135.636 + 78.3093i) q^{96} +(-63.9772 - 110.812i) q^{97} -105.636 q^{98} +(-227.204 - 131.176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9}+O(q^{10}) \) 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9	\( 4 q + 8 q^{2} - 6 q^{3} + 16 q^{4} - 4 q^{5} - 12 q^{6} + 32 q^{8} + 8 q^{9} - 8 q^{10} - 24 q^{12} - 12 q^{13} - 48 q^{15} + 64 q^{16} - 32 q^{17} + 16 q^{18} + 42 q^{19} - 16 q^{20} - 44 q^{21} + 12 q^{23} - 48 q^{24} - 18 q^{25} - 24 q^{26} - 4 q^{29} - 96 q^{30} + 128 q^{32} + 106 q^{33} - 64 q^{34} - 12 q^{35} + 32 q^{36} - 96 q^{37} + 84 q^{38} - 32 q^{40} + 26 q^{41} - 88 q^{42} - 72 q^{43} + 208 q^{45} + 24 q^{46} - 96 q^{48} - 36 q^{49} - 36 q^{50} - 24 q^{51} - 48 q^{52} + 124 q^{53} + 288 q^{55} + 124 q^{57} - 8 q^{58} - 78 q^{59} - 192 q^{60} - 44 q^{61} + 216 q^{63} + 256 q^{64} + 48 q^{65} + 212 q^{66} - 102 q^{67} - 128 q^{68} - 384 q^{69} - 24 q^{70} + 204 q^{71} + 64 q^{72} - 26 q^{73} - 192 q^{74} + 168 q^{76} + 248 q^{77} - 360 q^{79} - 64 q^{80} - 38 q^{81} + 52 q^{82} - 176 q^{84} - 184 q^{85} - 144 q^{86} - 16 q^{89} + 416 q^{90} - 144 q^{91} + 48 q^{92} - 80 q^{93} + 24 q^{95} - 192 q^{96} - 234 q^{97} - 72 q^{98} - 624 q^{99}+O(q^{100}) \) 4 * q + 8 * q^2 - 6 * q^3 + 16 * q^4 - 4 * q^5 - 12 * q^6 + 32 * q^8 + 8 * q^9 - 8 * q^10 - 24 * q^12 - 12 * q^13 - 48 * q^15 + 64 * q^16 - 32 * q^17 + 16 * q^18 + 42 * q^19 - 16 * q^20 - 44 * q^21 + 12 * q^23 - 48 * q^24 - 18 * q^25 - 24 * q^26 - 4 * q^29 - 96 * q^30 + 128 * q^32 + 106 * q^33 - 64 * q^34 - 12 * q^35 + 32 * q^36 - 96 * q^37 + 84 * q^38 - 32 * q^40 + 26 * q^41 - 88 * q^42 - 72 * q^43 + 208 * q^45 + 24 * q^46 - 96 * q^48 - 36 * q^49 - 36 * q^50 - 24 * q^51 - 48 * q^52 + 124 * q^53 + 288 * q^55 + 124 * q^57 - 8 * q^58 - 78 * q^59 - 192 * q^60 - 44 * q^61 + 216 * q^63 + 256 * q^64 + 48 * q^65 + 212 * q^66 - 102 * q^67 - 128 * q^68 - 384 * q^69 - 24 * q^70 + 204 * q^71 + 64 * q^72 - 26 * q^73 - 192 * q^74 + 168 * q^76 + 248 * q^77 - 360 * q^79 - 64 * q^80 - 38 * q^81 + 52 * q^82 - 176 * q^84 - 184 * q^85 - 144 * q^86 - 16 * q^89 + 416 * q^90 - 144 * q^91 + 48 * q^92 - 80 * q^93 + 24 * q^95 - 192 * q^96 - 234 * q^97 - 72 * q^98 - 624 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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